6.1 What is a Polygon?

Size: px
Start display at page:

Download "6.1 What is a Polygon?"

Transcription

1 6. What is a Polygon? Unit 6 Polygons and Quadrilaterals Regular polygon - Polygon Names: # sides Name 3 4 raw hexagon RPTOE Name the vertices: Name the sides: Name the diagonals containing R Name 2 consecutive <s Name 2 consecutive sides 2 n

2 Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides For a polygon to be regular, it must be both equiangular and equilateral. Name the only type of polygon that must be regular if it is equiangular. Tell whether each polygon is regular or irregular. Then tell whether it is concave or convex Find the sum of the interior angle measures of a 4-gon. 9. Find the measure of each interior angle of hexagon EF. 0. Find the value of n in pentagon PQRST. Polygon Formulas: (n = # of sides) One interior angle: 80(n 2) n Sum of the interior angles of a polygon = One interior angle 360 = One exterior angle: n Sum of the exterior angles of a polygon = One exterior angle = Polygon Practice:. Find the sum of the measures of the angles of a convex polygon with 4 sides. 2. For the given regular polygon, find the measure of each of its interior angles: a) dodecagon b) 6 gon 3. Find the degree measure of each exterior angle of a regular polygon with 20 sides. 4. For the following measures of an angle of a regular polygon, find the number of sides. a) 60 b) The sum of the interior angles of a convex polygon is Find the number of sides. 6. Find the number of sides of a regular polygon if the measure of one of its interior angles is three times the measure of its adjacent exterior angle. Find the sum of the measures of the angles of a convex polygon with the given # of sides

3 For each of the following, the measure of one angle of a regular convex polygon is given. Find the # of sides For each of the following, the number of sides of a regular polygon is given. Find the measure of each angle Find the degree measure of one exterior angle for a regular polygon with the given # of sides The sum of the measure of the interior angles of a convex polygon is 260. lassify the polygon. 6. The measure of one exterior angle of a regular polygon is 45. lassify the polygon. 7. Find the number of sides of a regular polygon, if the measure of one of its interior angles equals the measure of its adjacent exterior angle. 8. Find the number of sides of a regular polygon, if the measure of one of its interior angles equals twice the measure of the adjacent exterior angle. 9. lassify the regular polygon, if the measure of one of its interior angles equals one-half the measure of the adjacent exterior angle. 20. If the sum of the measures of six interior angles of a heptagon is 755, what is the measure of the remaining angle? Quadrilateral is any 4-sided polygon. The sum of interior angles for every quadrilateral is 360 Example. m< = 27 Solve for x and y. 2 m< = 38 m< = E Find each measure. True/False. Every parallelogram is a quadrilateral. 2. Every quadrilateral is a parallelogram. 3. ll angles of a parallelogram are congruent. 4. Opposite sides of a parallelogram are always congruent. 5. In PEX, PX P //. 6. In RY, Y R. 7. In TO, T and O bisect each other. 3

4 Proving a Quadrilateral is a parallelogram quadrilateral is a parallelogram if:. both pairs of opposite sides are parallel (by definition) State whether the given information is sufficient to support the statement, Quadrilateral is a parallelogram. If the information is sufficient, state the reason. 4

5 Proofs! ) Given: 2; 3 4 Prove: QRST is a parallelogram T 2 4 S Q 3 R 2) Given: 2, E E Prove: is a Parallelogram E 2 3) Given: PQRS PJ RK S K R Prove: SJ QK P J Q Q X R 4) Given: QRST; QXYZ Prove: Y S T Z Y S 5) Given: Ð, Ð Prove: E is a parallelogram E 6) 5

6 Rectangles efinition: rectangle is a quadrilateral with. efinition: rectangle is a parallelogram with. To prove that a quadrilateral is a rectangle, prove that: ) It is a quadrilateral with. 2) It is a parallelogram with. 3) It is a parallelogram with. Which of the following quadrilaterals are rectangles? Justify your answer For 4 0, is a parallelogram. From the information given, tell whether is a rectangle. 4. Given: 5. Given: 6. Given: is a right angle. 7. Given: 8. Given: 9. Given: 0. Given: ; is a right angle. Find x and y Given: iagonals RP and SQ of rectangle PQRS meet at M. If PM = x + 3y, SM = 4y 2x and RM = 20. Rhombus efinition: quadrilateral is a rhombus iff. efinition: parallelogram is a rhombus iff. H Mark the rhombus. How many s? What must be true about HO? R O The m<rh = 23ᵒ. Find the measure of the remaining interior angles. M 6

7 Which of the following are rhombuses? Justify each answer For 4 0, is a parallelogram. From the info. Given tell whether is a rhombus. 4. Given: 5. Given: 6. Given: is a right angle 7. Given: 8. Given: ; is a right angle 9. Given: 0. Given:. In rhombus, m = 3x 5 and m = x 3. Find the measures of all the angles of the rhombus. 2. In parallelogram, = 7x 3, = 3x + 5, and = 4x Find the lengths of the sides of parallelogram. What type of parallelogram is? parallelogram is a square iff it has one right angle and 2 adjacent sides square is both a and a. square has all of the properties of a,, and. To prove a quadrilateral is a square, prove that: ) It is a rectangle with. 2) It is a rectangle with. 3) It is a rectangle with. E 4) It is a rhombus with. 5) It is a rhombus with. 6) It is a parallelogram with. True or False. 7

8 7. ll rhombi are parallelograms. 8. Some rectangles are squares. 9. ll parallelograms are rectangles. 0. Some rhombi are rectangles.. ll rectangles are squares. 2. ll squares are rectangles. 3. Some squares are rectangles. Use square and the given information to find each value. 4. If m E = 3x, find x. 5. If m = 9x, find x. 6. If = 2x + and = 3x 5, find 7. If m = y and m = 3x, find x and y. 8. If = x 2-5 and = 2x, find x. E 6.6 Kites and Trapezoids kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. Properties: y 6x x 2 Find the value(s) of the variable(s) in each kite (x+6) 5y 2x (2x-4) y (3x+5) (4x- 30) (2y-20) an two angles of a kite be as follows? 7. opposite and acute 8. consecutive and obtuse 9. opposite and supplementary 0. consecutive and supplementary. opposite and complementary 2. consecutive and complementary 3. The perimeter of a kite is 66 cm. The length of one of its sides is 3 cm less that twice the length of another. Find the length of each side of the kite. 8

9 Trapezoids trapezoid is a quadrilateral with exactly two parallel sides. Leg Isosceles Trapezoid: trapezoid with congruent legs. Theorem: The base angles of an isosceles trapezoid are congruent. Theorem: The diagonals of an isosceles trapezoid are congruent. Every trapezoid contains two pairs of consecutive angles that are supplementary. as as Leg Example : Given the trapezoid HLJK. If the measure of angles H and L. m J 65 and the m K 95, the Example 2: Use Isosceles Trapezoid with length of =. // a. m = 75. Find the m. b. = 40. Find. c. If m 6x 25 and m 8x 5, find the measures of angle and. Median line segment connecting the midpoints of the legs of a trapezoid. The median is parallel to the bases. Theorem: The length of the median of a trapezoid equals one-half the sum of the bases. m 2 b b 2 Example 3: HJKL is an isosceles trapezoid with bases HJ and LK, and median RS. Use the given information to solve each problem. a. LK = 30, HJ = 42, find RS b. RS = 7, HJ = 4, Find LK. L K c. RS = x + 5, HJ + LK = 4x + 6 find RS R H J S 9

10 Example 4: 5x + 2 Find the length of each side of the isosceles trapezoid below. 6x x 4x lgebraic Formulas Used to etermine the Type of Quadrilateral To Show that a quadrilateral is a Parallelogram Method : oth pairs of opposite sides are congruent (find distance) Method 2: oth pairs of opposite sides are parallel (find slope) Method 3: One pair of opposite sides are both parallel and congruent (find distance and slope) To show that a quadrilateral is a Rhombus ****FIRST show that it is a parallelogram**** Method : ll 4 sides are congruent Method 2: iagonals are perpendicular (find slope of diagonals) To show that a quadrilateral is a Rectangle ****FIRST show that it is a parallelogram**** Method : ll angles are right angles Method 2: iagonals are congruent (find distance of diagonals) To show that a quadrilateral is an Isosceles Trapezoid Graph first o Legs are congruent (find distance) o ases are parallel (find slope) iagonals are congruent To show that a quadrilateral is a Kite Two pairs of consecutive congruent sides that are not congruent to each other (find the distance) 0

11 Practice etermining Quadrilaterals (Most Precise Name) ) Given quadrilateral with coordinates (-, -2), (4, 4), (0, -), and (5, -7). Is quad a rectangle? (Note: Use the slope formula.) Slope of = Slope of = Slope of = Slope of = 2) The coordinates of quadrilateral QRST are: Q (-2, -), R (-, 2), S (2, 3), and T (, 0). a) Find the slopes of the diagonals of quad QRST. re they perpendicular? Slope of QS = Slope of RT = b) Find the midpoints of each of the diagonals. Midpoint of QS = (, ) Midpoint of RT = (, ) o they bisect each other? Why or why not? c) What are all the possible classifications for quad QRST? d) The most precise name? 3) Given: (-,-6), (,-3), (, ) and (9,-2) Show that Quad. is a parallelogram. 4) Given: EFGH is a parallelogram with E(-4,), F(2,3), G(4,9) and H(-2,7) Show that EFGH is a rhombus. 5) Given: RSTU is a parallelogram with R (-4, 5), S (-, 9), T (7, 3) and U (4,-) Show that RSTU is a rectangle. 6) Given: Quad. with (6,-4), (6, 2), (3, 2) and (3,-4). Is this a parallelogram?

12 For #7 9, use slope, midpoint and/or the distance formulas to determine the most precise name for the quadrilateral with the given vertices. 7) (-4, 3), (-4, 8), (3, 0) (3, 5) 8) (-3, 7), (, 0), (, 5), (-3, 2) 9) (6, -5), (3, 0), (0, -5), (3, -9) 0) (-3, -3), (3, 4), (5, 0), (-4, -) ) (6, 0), (0, 6), (-6, 0), (0, -6) 2

Unit 6 Polygons and Quadrilaterals

Unit 6 Polygons and Quadrilaterals 6.1 What is a Polygon? A closed plane figure formed by segments that intersect only at their endpoints Regular Polygon- a polygon that is both equiangular and equilateral Unit 6 Polygons and Quadrilaterals

More information

Geometry/Trigonometry Unit 5: Polygon Notes Period:

Geometry/Trigonometry Unit 5: Polygon Notes Period: Geometry/Trigonometry Unit 5: Polygon Notes Name: Date: Period: # (1) Page 270 271 #8 14 Even, #15 20, #27-32 (2) Page 276 1 10, #11 25 Odd (3) Page 276 277 #12 30 Even (4) Page 283 #1-14 All (5) Page

More information

Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms

Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms Lesson 4.3 Ways of Proving that Quadrilaterals are Parallelograms Getting Ready: How will you know whether or not a figure is a parallelogram? By definition, a quadrilateral is a parallelogram if it has

More information

Geometry. Kites Families of Quadrilaterals Coordinate Proofs Proofs. Click on a topic to

Geometry. Kites Families of Quadrilaterals Coordinate Proofs Proofs. Click on a topic to Geometry Angles of Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Constructing Parallelograms Rhombi, Rectangles and Squares Kites Families of Quadrilaterals Coordinate

More information

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex.

Polygon. Note: Each segment is called a side. Each endpoint is called a vertex. Polygons Polygon A closed plane figure formed by 3 or more segments. Each segment intersects exactly 2 other segments at their endpoints. No 2 segments with a common endpoint are collinear. Note: Each

More information

Geometry. Quadrilaterals. Slide 1 / 189. Slide 2 / 189. Slide 3 / 189. Table of Contents. New Jersey Center for Teaching and Learning

Geometry. Quadrilaterals. Slide 1 / 189. Slide 2 / 189. Slide 3 / 189. Table of Contents. New Jersey Center for Teaching and Learning New Jersey enter for Teaching and Learning Slide 1 / 189 Progressive Mathematics Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students

More information

Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º.

Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º. Definition: Convex polygon A convex polygon is a polygon in which the measure of each interior angle is less than 180º. Definition: Convex polygon A convex polygon is a polygon in which the measure of

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name ate hapter 7 Maintaining Mathematical Proficiency Solve the equation by interpreting the expression in parentheses as a single quantity. 1. 5( 10 x) = 100 2. 6( x + 8) 12 = 48 3. ( x) ( x) 32 + 42

More information

A closed plane figure with at least 3 sides The sides intersect only at their endpoints. Polygon ABCDEF

A closed plane figure with at least 3 sides The sides intersect only at their endpoints. Polygon ABCDEF A closed plane figure with at least 3 sides The sides intersect only at their endpoints B C A D F E Polygon ABCDEF The diagonals of a polygon are the segments that connects one vertex of a polygon to another

More information

Polygon notes

Polygon notes 1.6-6.1 Polygon notes Polygon: Examples: Nonexamples: Named by the letters of the vertices written in order polygon will be: oncave - Or: onvex- Regular Polygon: 1.6-6.1 Polygon notes iagonal is a segment

More information

CC Geometry H Do Now: Complete the following: Quadrilaterals

CC Geometry H Do Now: Complete the following: Quadrilaterals im #26: What are the properties of parallelograms? Geometry H o Now: omplete the following: Quadrilaterals Kite iagonals are perpendicular One pair of opposite angles is congruent Two distinct pairs of

More information

8.1 Find Angle Measures in Polygons

8.1 Find Angle Measures in Polygons VOCABULARY 8.1 Find Angle Measures in Polygons DIAGONAL Review: EQUILATERAL EQUIANGULAR REGULAR CLASSIFYING POLYGONS Polygon Interior Angle Theorem: The sum of the measures of the interior angles of a

More information

Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x.

Problems #1. A convex pentagon has interior angles with measures (5x 12), (2x + 100), (4x + 16), (6x + 15), and (3x + 41). Find x. 1 Pre-AP Geometry Chapter 10 Test Review Standards/Goals: G.CO.11/ C.1.i.: I can use properties of special quadrilaterals in a proof. D.2.g.: I can identify and classify quadrilaterals, including parallelograms,

More information

U4 Polygon Notes January 11, 2017 Unit 4: Polygons

U4 Polygon Notes January 11, 2017 Unit 4: Polygons Unit 4: Polygons 180 Complimentary Opposite exterior Practice Makes Perfect! Example: Example: Practice Makes Perfect! Def: Midsegment of a triangle - a segment that connects the midpoints of two sides

More information

6-1 Study Guide and Intervention Angles of Polygons

6-1 Study Guide and Intervention Angles of Polygons 6-1 Study Guide and Intervention Angles of Polygons Polygon Interior Angles Sum The segments that connect the nonconsecutive vertices of a polygon are called diagonals. Drawing all of the diagonals from

More information

Polygons are named by the number of sides they have:

Polygons are named by the number of sides they have: Unit 5 Lesson 1 Polygons and Angle Measures I. What is a polygon? (Page 322) A polygon is a figure that meets the following conditions: It is formed by or more segments called, such that no two sides with

More information

Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review

Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Polygon a closed plane figure with at least 3 sides that are segments -the sides do not intersect except at the vertices N-gon -

More information

Any questions about the material so far? About the exercises?

Any questions about the material so far? About the exercises? Any questions about the material so far? About the exercises? Here is a question for you. In the diagram on the board, DE is parallel to AC, DB = 4, AB = 9 and BE = 8. What is the length EC? Polygons Definitions:

More information

Vocabulary. Term Page Definition Clarifying Example base angle of a trapezoid. base of a trapezoid. concave (polygon) convex (polygon)

Vocabulary. Term Page Definition Clarifying Example base angle of a trapezoid. base of a trapezoid. concave (polygon) convex (polygon) HPTER 6 Vocabulary The table contains important vocabulary terms from hapter 6. s you work through the chapter, fill in the page number, definition, and a clarifying example. Term Page efinition larifying

More information

Examples: Identify the following as equilateral, equiangular or regular. Using Variables: S = 180(n 2)

Examples: Identify the following as equilateral, equiangular or regular. Using Variables: S = 180(n 2) Ch. 6 Notes 6.1: Polygon Angle-Sum Theorems Examples: Identify the following as equilateral, equiangular or regular. 1) 2) 3) S = 180(n 2) Using Variables: and Examples: Find the sum of the interior angles

More information

Chapter 8. Quadrilaterals

Chapter 8. Quadrilaterals Chapter 8 Quadrilaterals 8.1 Find Angle Measures in Polygons Objective: Find angle measures in polygons. Essential Question: How do you find a missing angle measure in a convex polygon? 1) Any convex polygon.

More information

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means

Period: Date Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means : Analytic Proofs of Theorems Previously Proved by Synthetic Means Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of

More information

14. How many sides does a regular polygon have, if the measure of an interior angle is 60?

14. How many sides does a regular polygon have, if the measure of an interior angle is 60? State whether the figure is a polygon; if it is a polygon, state whether the polygon is convex or concave. HINT: No curves, no gaps, and no overlaps! 1. 2. 3. 4. Find the indicated measures of the polygon.

More information

1. Revision Description Reflect and Review Teasers Answers Recall of basics of triangles, polygons etc. Review Following are few examples of polygons:

1. Revision Description Reflect and Review Teasers Answers Recall of basics of triangles, polygons etc. Review Following are few examples of polygons: 1. Revision Recall of basics of triangles, polygons etc. The minimum number of line segments required to form a polygon is 3. 1) Name the polygon formed with 4 line segments of equal length. 1) Square

More information

Geometry Review for Test 3 January 13, 2016

Geometry Review for Test 3 January 13, 2016 Homework #7 Due Thursday, 14 January Ch 7 Review, pp. 292 295 #1 53 Test #3 Thurs, 14 Jan Emphasis on Ch 7 except Midsegment Theorem, plus review Betweenness of Rays Theorem Whole is Greater than Part

More information

Angles of Polygons Concept Summary

Angles of Polygons Concept Summary Vocabulary and oncept heck diagonal (p. 404) isosceles trapezoid (p. 439) kite (p. 438) median (p. 440) parallelogram (p. 411) rectangle (p. 424) rhombus (p. 431) square (p. 432) trapezoid (p. 439) complete

More information

CHAPTER 6. SECTION 6-1 Angles of Polygons POLYGON INTERIOR ANGLE SUM

CHAPTER 6. SECTION 6-1 Angles of Polygons POLYGON INTERIOR ANGLE SUM HPTER 6 Quadrilaterals SETION 6-1 ngles of Polygons POLYGON INTERIOR NGLE SUM iagonal - a line segment that connects two nonconsecutive vertices. Polygon interior angle sum theorem (6.1) - The sum of the

More information

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles

6.1: Date: Geometry. Polygon Number of Triangles Sum of Interior Angles 6.1: Date: Geometry Polygon Number of Triangles Sum of Interior Angles Triangle: # of sides: # of triangles: Quadrilateral: # of sides: # of triangles: Pentagon: # of sides: # of triangles: Hexagon: #

More information

Geometry. Slide 1 / 343. Slide 2 / 343. Slide 3 / 343. Quadrilaterals. Table of Contents

Geometry. Slide 1 / 343. Slide 2 / 343. Slide 3 / 343. Quadrilaterals. Table of Contents Slide 1 / 343 Slide 2 / 343 Geometry Quadrilaterals 2015-10-27 www.njctl.org Table of ontents Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Rhombi, Rectangles and Squares

More information

Secondary Math II Honors. Unit 4 Notes. Polygons. Name: Per:

Secondary Math II Honors. Unit 4 Notes. Polygons. Name: Per: Secondary Math II Honors Unit 4 Notes Polygons Name: Per: Day 1: Interior and Exterior Angles of a Polygon Unit 4 Notes / Secondary 2 Honors Vocabulary: Polygon: Regular Polygon: Example(s): Discover the

More information

Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets

Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Lesson 9: Coordinate Proof - Quadrilaterals Learning Targets Using coordinates, I can find the intersection of the medians of a triangle that meet at a point that is two-thirds of the way along each median

More information

Polygon Interior Angles

Polygon Interior Angles Polygons can be named by the number of sides. A regular polygon has All other polygons are irregular. A concave polygon has All other polygons are convex, with all vertices facing outwards. Name each polygon

More information

Geometry Lesson 1 Introduction to Geometry (Grades 9-12) Instruction 1-5 Definitions of Figures

Geometry Lesson 1 Introduction to Geometry (Grades 9-12) Instruction 1-5 Definitions of Figures efinitions of igures Quadrilaterals Quadrilaterals are closed four-sided figures. The interior angles of a quadrilateral always total 360. Quadrilaterals classified in two groups: Trapeziums and Trapezoids.

More information

RPDP Geometry Seminar Quarter 1 Handouts

RPDP Geometry Seminar Quarter 1 Handouts RPDP Geometry Seminar Quarter 1 Handouts Geometry lassifying Triangles: State Standard 4.12.7 4.12.9 Syllabus Objectives: 5.11, 6.1, 6.4, 6.5 enchmarks: 2 nd Quarter - November Find the distance between:

More information

5. Trapezoid: Exactly one pair of parallel sides. 6. Isosceles Trapezoid is a trapezoid where the non-parallel sides are equal.

5. Trapezoid: Exactly one pair of parallel sides. 6. Isosceles Trapezoid is a trapezoid where the non-parallel sides are equal. Quadrilaterals page #1 Five common types of quadrilaterals are defined below: Mark each picture: 1. Parallelogram: oth pairs of opposite sides parallel. 2. Rectangle: Four right angles. 3. Rhombus: Four

More information

22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Chapter 4 Quadrilaterals 4.1 Properties of a Parallelogram Definitions 22. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. 23. An altitude of a parallelogram is the

More information

Geometry Ch 7 Quadrilaterals January 06, 2016

Geometry Ch 7 Quadrilaterals January 06, 2016 Theorem 17: Equal corresponding angles mean that lines are parallel. Corollary 1: Equal alternate interior angles mean that lines are parallel. Corollary 2: Supplementary interior angles on the same side

More information

Honors Geometry. Worksheet 4.1: Quadrilaterals. Quadrilateral:. (definition) Parallelogram:. (definition)

Honors Geometry. Worksheet 4.1: Quadrilaterals. Quadrilateral:. (definition) Parallelogram:. (definition) Honors Geometry Name: Worksheet 4.1: Quadrilaterals Fill in the blanks using definitions and theorems about quadrilaterals. Quadrilateral:. The midquad of a quadrilateral is a. The sum of the measures

More information

Geometry Chapter 8 Test Review

Geometry Chapter 8 Test Review Geometry Chapter 8 Test Review Short Answer 1. Find the sum of the measures of the interior angles of the indicated convex polygon. Decagon 2. Find the sum of the measures of the interior angles of the

More information

Pre-AICE 2: Unit 5 Exam - Study Guide

Pre-AICE 2: Unit 5 Exam - Study Guide Pre-AICE 2: Unit 5 Exam - Study Guide 1 Find the value of x. (The figure may not be drawn to scale.) A. 74 B. 108 C. 49 D. 51 2 Find the measure of an interior angle and an exterior angle of a regular

More information

Unit 5: Polygons and Quadrilaterals

Unit 5: Polygons and Quadrilaterals Unit 5: Polygons and Quadrilaterals Scale for Unit 5 4 Through independent work beyond what was taught in class, students could (examples include, but are not limited to): - Research a unique building

More information

Math Polygons

Math Polygons Math 310 9.2 Polygons Curve & Connected Idea The idea of a curve is something you could draw on paper without lifting your pencil. The idea of connected is that a set can t be split into two disjoint sets.

More information

8 sides 17 sides. x = 72

8 sides 17 sides. x = 72 GEOMETRY Chapter 7 Review Quadrilaterals Name: Hour: Date: SECTION 1: State whether each polygon is equilateral, equiangular, or regular. 1) 2) 3) equilateral regular equiangular SECTION 2: Calculate the

More information

Geometry Unit 5 - Notes Polygons

Geometry Unit 5 - Notes Polygons Geometry Unit 5 - Notes Polygons Syllabus Objective: 5.1 - The student will differentiate among polygons by their attributes. Review terms: 1) segment 2) vertex 3) collinear 4) intersect Polygon- a plane

More information

INTUITIVE GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY

INTUITIVE GEOMETRY SEMESTER 1 EXAM ITEM SPECIFICATION SHEET & KEY INTUITIVE GEOMETRY SEMESTER EXM ITEM SPEIFITION SHEET & KEY onstructed Response # Objective Syllabus Objective NV State Standard istinguish among the properties of various quadrilaterals. 7. 4.. lassify

More information

Slide 1 / 343 Slide 2 / 343

Slide 1 / 343 Slide 2 / 343 Slide 1 / 343 Slide 2 / 343 Geometry Quadrilaterals 2015-10-27 www.njctl.org Slide 3 / 343 Table of ontents Polygons Properties of Parallelograms Proving Quadrilaterals are Parallelograms Rhombi, Rectangles

More information

Geometry Honors. Midterm Review

Geometry Honors. Midterm Review eometry onors Midterm Review lass: ate: eometry onors Midterm Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1 What is the contrapositive of the statement

More information

Capter 6 Review Sheet. 1. Given the diagram, what postulate or theorem would be used to prove that AP = CP?

Capter 6 Review Sheet. 1. Given the diagram, what postulate or theorem would be used to prove that AP = CP? apter 6 Review Sheet Name: ate: 1. Given the diagram, what postulate or theorem would be used to prove that P = P? 4.. S. SSS.. SS 2. Given the diagram, what postulate or theorem would be used to prove

More information

Geometry Honors. Midterm Review

Geometry Honors. Midterm Review eometry Honors Midterm Review lass: ate: I: eometry Honors Midterm Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1 What is the contrapositive of the

More information

Unit 9: Quadrilaterals

Unit 9: Quadrilaterals Unit 9: Quadrilaterals Topic/Assignment I CAN statement Turned in? Properties of Quadrilaterals HW: Worksheet Properties of all Quadrilaterals Properties of Parallelograms HW: Properties of Parallelograms

More information

B. Algebraic Properties Reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division

B. Algebraic Properties Reflexive, symmetric, transitive, substitution, addition, subtraction, multiplication, division . efinitions 1) cute angle ) cute triangle 3) djacent angles 4) lternate exterior angles 5) lternate interior angles 6) ltitude of a triangle 7) ngle ) ngle bisector of a triangle 9) ngles bisector 10)

More information

Unit 3: Triangles and Polygons

Unit 3: Triangles and Polygons Unit 3: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about triangles. Objective: By the end of class, I should Example 1: Trapezoid on the coordinate plane below has the following

More information

Geometry Third Quarter Study Guide

Geometry Third Quarter Study Guide Geometry Third Quarter Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,

More information

Angle Unit Definitions

Angle Unit Definitions ngle Unit Definitions Name lock Date Term Definition Notes Sketch D djacent ngles Two coplanar angles with a coon side, a coon vertex, and no coon interior points. Must be named with 3 letters OR numbers

More information

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Four sided polygon 1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line. Foldable Foldable The fold crease 2. Now, divide the right hand section

More information

Geometry Chapter 5 Review Sheet

Geometry Chapter 5 Review Sheet Geometry hapter 5 Review Sheet Name: 1. List the 6 properties of the parallelogram. 2. List the 5 ways to prove that a quadrilateral is a parallelogram. 3. Name two properties of the rectangle that are

More information

Unit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook

Unit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook Unit 2: Triangles and Quadrilaterals Lesson 2.1 pply Triangle Sum Properties Lesson 4.1 from textbook Objectives Classify angles by their sides as equilateral, isosceles, or scalene. Classify triangles

More information

8 Quadrilaterals. Before

8 Quadrilaterals. Before 8 Quadrilaterals 8. Find Angle Measures in Polygons 8. Use Properties of Parallelograms 8.3 Show that a Quadrilateral is a Parallelogram 8.4 Properties of Rhombuses, Rectangles, and Squares 8.5 Use Properties

More information

Geometry Reasons for Proofs Chapter 1

Geometry Reasons for Proofs Chapter 1 Geometry Reasons for Proofs Chapter 1 Lesson 1.1 Defined Terms: Undefined Terms: Point: Line: Plane: Space: Postulate 1: Postulate : terms that are explained using undefined and/or other defined terms

More information

Proving Theorems about Lines and Angles

Proving Theorems about Lines and Angles Proving Theorems about Lines and Angles Angle Vocabulary Complementary- two angles whose sum is 90 degrees. Supplementary- two angles whose sum is 180 degrees. Congruent angles- two or more angles with

More information

Name Date Class. The Polygon Angle Sum Theorem states that the sum of the interior angle measures of a convex polygon with n sides is (n 2)180.

Name Date Class. The Polygon Angle Sum Theorem states that the sum of the interior angle measures of a convex polygon with n sides is (n 2)180. Name Date Class 6-1 Properties and Attributes of Polygons continued The Polygon Angle Sum Theorem states that the sum of the interior angle measures of a convex polygon with n sides is (n 2)180. Convex

More information

Review Unit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary.

Review Unit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. Worksheet by Kuta oftware LLC -1- Geometry Review nit 5 t Find the measure of one interior angle in each regular polygon. Round your answer to the nearest tenth if necessary. 1) 2) regular 18-gon Find

More information

Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday & 6-3.

Dates, assignments, and quizzes subject to change without advance notice. Monday Tuesday Block Day Friday & 6-3. Name: Period P UNIT 11: QURILTERLS N POLYONS I can define, identify and illustrate the following terms: Quadrilateral Parallelogram Rhombus Rectangle Square Trapezoid Isosceles trapezoid Kite oncave polygon

More information

Geometry Basics of Geometry Precise Definitions Unit CO.1 OBJECTIVE #: G.CO.1

Geometry Basics of Geometry Precise Definitions Unit CO.1 OBJECTIVE #: G.CO.1 OBJECTIVE #: G.CO.1 OBJECTIVE Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance

More information

CHAPTER 8 QUADRILATERALS

CHAPTER 8 QUADRILATERALS HTE 8 UILTEL In this chapter we address three ig IE: ) Using angle relationships in polygons. ) Using properties of parallelograms. 3) lassifying quadrilaterals by the properties. ection: Essential uestion

More information

Polygons, Congruence, Similarity Long-Term Memory Review Grade 8 Review 1

Polygons, Congruence, Similarity Long-Term Memory Review Grade 8 Review 1 Review 1 1. In the diagram below, XYZ is congruent to CDE XYZ CDE. Y D E X Z C Complete the following statements: a) C b) XZ c) CDE d) YZ e) Z f) DC 2. In the diagram below, ABC is similar to DEF ABC DEF.

More information

Triangle Geometry Isometric Triangles Lesson 1

Triangle Geometry Isometric Triangles Lesson 1 Triangle eometry Isometric Triangles Lesson 1 Review of all the TORMS in OMTRY that you know or soon will know!. Triangles 1. The sum of the measures of the interior angles of a triangle is 180º (Triangle

More information

Lines Plane A flat surface that has no thickness and extends forever.

Lines Plane A flat surface that has no thickness and extends forever. Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that

More information

Understanding Quadrilaterals

Understanding Quadrilaterals Understanding Quadrilaterals Parallelogram: A quadrilateral with each pair of opposite sides parallel. Properties: (1) Opposite sides are equal. (2) Opposite angles are equal. (3) Diagonals bisect one

More information

NAME DATE PERIOD. A#1: Angles of Polygons

NAME DATE PERIOD. A#1: Angles of Polygons NAME DATE PERIOD A#1: Angles of Polygons Angle Sum of a Regular or Irregular Polygon Interior Angles Exterior Angles One Angle Measure of a Regular Polygon Find the sum of the measures of the interior

More information

Assumption High School. Bell Work. Academic institution promoting High expectations resulting in Successful students

Assumption High School. Bell Work. Academic institution promoting High expectations resulting in Successful students Bell Work Geometry 2016 2017 Day 36 Topic: Chapter 4 Congruent Figures Chapter 6 Polygons & Quads Chapter 4 Big Ideas Visualization Visualization can help you connect properties of real objects with two-dimensional

More information

Points, lines, angles

Points, lines, angles Points, lines, angles Point Line Line segment Parallel Lines Perpendicular lines Vertex Angle Full Turn An exact location. A point does not have any parts. A straight length that extends infinitely in

More information

Cambridge Essentials Mathematics Core 9 GM1.1 Answers. 1 a

Cambridge Essentials Mathematics Core 9 GM1.1 Answers. 1 a GM1.1 Answers 1 a b 2 Shape Name Regular Irregular Convex Concave A Decagon B Octagon C Pentagon D Quadrilateral E Heptagon F Hexagon G Quadrilateral H Triangle I Triangle J Hexagon Original Material Cambridge

More information

Postulates, Theorems, and Corollaries. Chapter 1

Postulates, Theorems, and Corollaries. Chapter 1 Chapter 1 Post. 1-1-1 Through any two points there is exactly one line. Post. 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Post. 1-1-3 If two points lie in a

More information

GEOMETRY COORDINATE GEOMETRY Proofs

GEOMETRY COORDINATE GEOMETRY Proofs GEOMETRY COORDINATE GEOMETRY Proofs Name Period 1 Coordinate Proof Help Page Formulas Slope: Distance: To show segments are congruent: Use the distance formula to find the length of the sides and show

More information

Int. Geometry Unit 7 Test Review 1

Int. Geometry Unit 7 Test Review 1 Int. Geometry Unit 7 est eview uestions -0: omplete each statement with sometimes, always, or never.. he diagonals of a trapezoid are congruent.. rhombus is equiangular.. rectangle is a square.. he opposite

More information

Unit 10 Study Guide: Plane Figures

Unit 10 Study Guide: Plane Figures Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece

More information

6 Polygons and. Quadrilaterals CHAPTER. Chapter Outline.

6 Polygons and. Quadrilaterals CHAPTER. Chapter Outline. www.ck12.org CHAPTER 6 Polygons and Quadrilaterals Chapter Outline 6.1 ANGLES IN POLYGONS 6.2 PROPERTIES OF PARALLELOGRAMS 6.3 PROVING QUADRILATERALS ARE PARALLELOGRAMS 6.4 RECTANGLES, RHOMBUSES AND SQUARES

More information

Name: Period 1/4/11 1/20/11 GH

Name: Period 1/4/11 1/20/11 GH Name: Period 1/4/11 1/20/11 UNIT 10: QURILTERLS N POLYONS I can define, identify and illustrate the following terms: Quadrilateral Parallelogram Rhombus Rectangle Square Trapezoid Isosceles trapezoid Kite

More information

Geometry Final Exam - Study Guide

Geometry Final Exam - Study Guide Geometry Final Exam - Study Guide 1. Solve for x. True or False? (questions 2-5) 2. All rectangles are rhombuses. 3. If a quadrilateral is a kite, then it is a parallelogram. 4. If two parallel lines are

More information

What is a(n); 2. acute angle 2. An angle less than 90 but greater than 0

What is a(n); 2. acute angle 2. An angle less than 90 but greater than 0 Geometry Review Packet Semester Final Name Section.. Name all the ways you can name the following ray:., Section.2 What is a(n); 2. acute angle 2. n angle less than 90 but greater than 0 3. right angle

More information

GEOMETRY is the study of points in space

GEOMETRY is the study of points in space CHAPTER 5 Logic and Geometry SECTION 5-1 Elements of Geometry GEOMETRY is the study of points in space POINT indicates a specific location and is represented by a dot and a letter R S T LINE is a set of

More information

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers

Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers 1.1 The Three Dimensions 1. Possible answer: You need only one number to describe the location of a point on a line. You need two numbers to describe the location of a point on a plane. 2. vary. Possible

More information

Unit 2: Triangles and Polygons

Unit 2: Triangles and Polygons Unit 2: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about lines and angles. Objective: By the end of class, I should Using the diagram below, answer the following questions. Line

More information

Quadrilaterals. Polygons Basics

Quadrilaterals. Polygons Basics Name: Quadrilaterals Polygons Basics Date: Objectives: SWBAT identify, name and describe polygons. SWBAT use the sum of the measures of the interior angles of a quadrilateral. A. The basics on POLYGONS

More information

Review for Quadrilateral Test

Review for Quadrilateral Test Review for Quadrilateral Test 1. How many triangles are formed by drawing diagonals from one vertex in the figure? Find the sum of the measures of the angles in the figure. a. 6, 1080 b. 7, 1260 c. 7,

More information

Reteaching Transversals and Angle Relationships

Reteaching Transversals and Angle Relationships Name Date Class Transversals and Angle Relationships INV Transversals A transversal is a line that intersects two or more coplanar lines at different points. Line a is the transversal in the picture to

More information

Chapter 6 Practice Test

Chapter 6 Practice Test Find the sum of the measures of the interior angles of each convex polygon. 1. hexagon A hexagon has six sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures.

More information

Homework Worksheets: Chapter 7 HW#36: Problems #1-17

Homework Worksheets: Chapter 7 HW#36: Problems #1-17 Homework Worksheets: Chapter 7 HW#36: Problems #1-17 1.) Which of the following in an eample of an undefined term:. ray B. segment C. line D. skew E. angle 3.) Identify a countereample to the given statement.

More information

Formal Geometry UNIT 6 - Quadrilaterals

Formal Geometry UNIT 6 - Quadrilaterals Formal Geometry UNIT 6 - Quadrilaterals 14-Jan 15-Jan 16-Jan 17-Jan 18-Jan Day 1 Day Day 4 Kites and Day 3 Polygon Basics Trapezoids Proving Parallelograms Day 5 Homefun: Parallelograms Pg 48 431 #1 19,

More information

Unit 1.5: Quadrilaterals: Day 5 Quadrilaterals Review

Unit 1.5: Quadrilaterals: Day 5 Quadrilaterals Review P1 Math 2 Unit 1.5: Quadrilaterals: ay 5 Quadrilaterals Review Name t our next class meeting, we will take a quiz on quadrilaterals. It is important that you can differentiate between the definition of

More information

Name Date Class. 6. In JKLM, what is the value of m K? A 15 B 57 A RS QT C QR ST

Name Date Class. 6. In JKLM, what is the value of m K? A 15 B 57 A RS QT C QR ST Name Date Class CHAPTER 6 Chapter Review #1 Form B Circle the best answer. 1. Which best describes the figure? 6. In JKLM, what is the value of m K? A regular convex heptagon B irregular convex heptagon

More information

theorems & postulates & stuff (mr. ko)

theorems & postulates & stuff (mr. ko) theorems & postulates & stuff (mr. ko) postulates 1 ruler postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of

More information

Index COPYRIGHTED MATERIAL. Symbols & Numerics

Index COPYRIGHTED MATERIAL. Symbols & Numerics Symbols & Numerics. (dot) character, point representation, 37 symbol, perpendicular lines, 54 // (double forward slash) symbol, parallel lines, 54, 60 : (colon) character, ratio of quantity representation

More information

6.6 trapezoids and kites 2016 ink.notebook. January 29, Page 30 Page Kites and Trapezoids. Trapezoid Examples and Practice.

6.6 trapezoids and kites 2016 ink.notebook. January 29, Page 30 Page Kites and Trapezoids. Trapezoid Examples and Practice. 6.6 trapezoids and kites 2016 ink.notebook January 29, 2018 Page 30 Page 29 6.6 Kites and Trapezoids Page 31 Page 32 Trapezoid Examples and Practice Page 33 1 Lesson Objectives Standards Lesson Notes Lesson

More information

Geometry Unit 6 Note Sheets Date Name of Lesson. 6.2 Parallelograms. 6.3 Tests for Parallelograms. 6.4 Rectangles. 6.5 Rhombi and Squares

Geometry Unit 6 Note Sheets Date Name of Lesson. 6.2 Parallelograms. 6.3 Tests for Parallelograms. 6.4 Rectangles. 6.5 Rhombi and Squares Date Name of Lesson 6.2 Parallelograms 6.3 Tests for Parallelograms 6.4 Rectangles 6.5 Rhombi and Squares 6.6 Trapezoids and Kites 1 Quadrilaterals Properties Property Parallelogram Rectangle Rhombus Square

More information

Geometry: A Complete Course

Geometry: A Complete Course Geometry: omplete ourse with Trigonometry) Module Progress Tests Written by: Larry. ollins Geometry: omplete ourse with Trigonometry) Module - Progress Tests opyright 2014 by VideotextInteractive Send

More information

Geometry Third Quarter Study Guide

Geometry Third Quarter Study Guide Geometry Third Quarter Study Guide 1. Write the if-then form, the converse, the inverse and the contrapositive for the given statement: All right angles are congruent. 2. Find the measures of angles A,

More information

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.

Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence. Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity

More information

SOL 6.13 Quadrilaterals

SOL 6.13 Quadrilaterals SOL 6.13 Quadrilaterals 6.13 The student will describe and identify properties of quadrilaterals. Understanding the Standard: A quadrilateral is a closed planar (two-dimensional) figure with four sides

More information