4.7 Use Isosceles and Equilateral
|
|
|
- Lesley Mervin Park
- 6 years ago
- Views:
Transcription
1 4.7 Use Isosceles and Equilateral Triangles oal p Use theorems about isosceles and equilateral triangles. Your Notes VOULRY Legs Vertex angle ase ase angles TEOREM 4.7: SE NLES TEOREM If two sides of a triangle are congruent, then the angles opposite them are congruent. If >, then >. TEOREM 4.8: ONVERSE OF SE NLES TEOREM If two angles of a triangle are congruent, then the sides opposite them are congruent. If >, then >. Example 1 pply the ase ngles Theorem In nf, F >. Name two congruent angles. F >, so by the ase ngles Theorem, >. F 112 Lesson 4.7 eometry Notetaking uide opyright olt McDougal. ll rights reserved.
2 4.7 Use Isosceles and Equilateral Triangles oal p Use theorems about isosceles and equilateral triangles. Your Notes VOULRY Legs The legs of an isosceles triangle are the two congruent sides. Vertex angle The vertex angle of an isosceles triangle is the angle formed by the legs. ase The base of an isosceles triangle is the side that is not a leg. ase angles The base angles of an isosceles triangle are the two angles adjacent to the base. TEOREM 4.7: SE NLES TEOREM If two sides of a triangle are congruent, then the angles opposite them are congruent. If >, then >. TEOREM 4.8: ONVERSE OF SE NLES TEOREM If two angles of a triangle are congruent, then the sides opposite them are congruent. If >, then >. Example 1 pply the ase ngles Theorem In nf, F >. Name two congruent angles. F >, so by the ase ngles Theorem, F >. F 112 Lesson 4.7 eometry Notetaking uide opyright olt McDougal. ll rights reserved.
3 The corollaries state that a triangle is equilateral if and only if it is equiangular. OROLLRY TO TE SE NLES TEOREM If a triangle is equilateral, then it is. OROLLRY TO TE ONVERSE OF SE NLES TEOREM If a triangle is equiangular, then it is. Example 2 Find measures in a triangle Find the measures of R, S, and T. R The diagram shows that nrst is. Therefore, by the orollary to the ase ngles Theorem, nrst is. So, m R 5 m S 5 m T. 3(m R) 5 Triangle Sum Theorem m R 5 Divide each side by 3. The measures of R, S, and T are all. S T Example 3 Use isosceles and equilateral triangles Find the values of x and y in the diagram. K You cannot use J to refer to LJM because three angles have J as their vertex. Step 1 Find the value of x. ecause M 8 njkl is, it is 2y also and J KL >. Therefore, x 5. x Step 2 Find the value of y. ecause JML >, LM >, and nlmj is isosceles. You know that LJ 5. LM 5 Definition of congruent segments 2y 5 Substitute 2y for LM and for LJ. y 5 Divide each side by 2. L opyright olt McDougal. ll rights reserved. Lesson 4.7 eometry Notetaking uide 113
4 The corollaries state that a triangle is equilateral if and only if it is equiangular. OROLLRY TO TE SE NLES TEOREM If a triangle is equilateral, then it is equiangular. OROLLRY TO TE ONVERSE OF SE NLES TEOREM If a triangle is equiangular, then it is equilateral. Example 2 Find measures in a triangle Find the measures of R, S, and T. R The diagram shows that nrst is equilateral. Therefore, by the orollary to the ase ngles Theorem, nrst is equiangular. So, m R 5 m S 5 m T. 3(m R) Triangle Sum Theorem m R Divide each side by 3. The measures of R, S, and T are all 608. S T Example 3 Use isosceles and equilateral triangles Find the values of x and y in the diagram. K You cannot use J to refer to LJM because three angles have J as their vertex. Step 1 Find the value of x. ecause M 8 njkl is equiangular, it is also equilateral and J KL > JL. Therefore, x y x Step 2 Find the value of y. ecause JML > LJM, LM > LJ, and nlmj is isosceles. You know that LJ 5 8. LM 5 LJ 2y 5 8 Definition of congruent segments Substitute 2y for LM and 8 for LJ. y 5 4 Divide each side by 2. L opyright olt McDougal. ll rights reserved. Lesson 4.7 eometry Notetaking uide 113
5 Example 4 Solve a multi-step problem Quilting The pattern at the right is present in a quilt. a. Explain why nd is equilateral. b. Show that n > nd. D a. y the ase ngles Theorem, D >. So, nd is. y the, nd is equilateral. b. y the ase ngles Theorem, >. So, n > nd by the. heckpoint omplete the following exercises. 1. opy and complete the statement: If F > FJ, then? >?. 2. opy and complete the statement: If nfk is equiangular and F 5 15, then K 5?. F K J 3. Use parts (a) and (b) in Example 4 to show that m D omework 114 Lesson 4.7 eometry Notetaking uide opyright olt McDougal. ll rights reserved.
6 Example 4 Solve a multi-step problem Quilting The pattern at the right is present in a quilt. a. Explain why nd is equilateral. b. Show that n > nd. D a. y the ase ngles Theorem, D > D. So, nd is equiangular. y the orollary to the onverse of ase ngles Theorem, nd is equilateral. b. y the ase ngles Theorem, >. So, n > nd by the S ongruence Theorem. heckpoint omplete the following exercises. 1. opy and complete the statement: If F > FJ, then? >?. ; J 2. opy and complete the statement: If nfk is equiangular and F 5 15, then K 5?. 15 F K J omework 3. Use parts (a) and (b) in Example 4 to show that m D nd is equiangular. So, m D 5 m D 5 m D. 3(m D) Triangle Sum Theorem m D Divide each side by 3. ecause nd is equiangular and n > nd, you know that m m D 5 m 1 m D Lesson 4.7 eometry Notetaking uide opyright olt McDougal. ll rights reserved.
There are three ways to classify triangles based on sides
Unit 4 Notes: Triangles 4-1 Triangle ngle-sum Theorem ngle review, label each angle with the correct classification: Triangle a polygon with three sides. There are two ways to classify triangles: by angles
4.2 Apply Congruence and
4.2 pply ongruence and riangles oal p Identify congruent figures. Your Notes VOULRY ongruent figures orresponding parts o help you identify corresponding parts, turn n. xample 1 Identify congruent parts
The side that is opposite the vertex angle is the base of the isosceles triangle.
Unit 5, Lesson 6. Proving Theorems about Triangles Isosceles triangles can be seen throughout our daily lives in structures, supports, architectural details, and even bicycle frames. Isosceles triangles
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
To use and apply properties of isosceles and equilateral triangles
- Isosceles and Equilateral riangles ontent Standards G.O. Prove theorems about triangles... base angles of isosceles triangles are congruent... lso G.O., G.SR. Objective o use and apply properties of
7.2 Isosceles and Equilateral Triangles
Name lass Date 7.2 Isosceles and Equilateral Triangles Essential Question: What are the special relationships among angles and sides in isosceles and equilateral triangles? Resource Locker Explore G.6.D
Maintaining Mathematical Proficiency
Name ate hapter 5 Maintaining Mathematical Proficiency Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. 1. ( 3, 1 ) and ( 5,
4-2 Triangle Congruence Conditions. Congruent Triangles - C F. and
4-2 Triangle ongruence onditions ongruent Triangles -,, ª is congruent to ª (ª ª) under a correspondence of parts if and only if 1) all three pairs of corresponding angles are congruent, and 2) all three
You try: What is the definition of an angle bisector? You try: You try: is the bisector of ABC. BD is the bisector of ABC. = /4.MD.
US Geometry 1 What is the definition of a midpoint? midpoint of a line segment is the point that bisects the line segment. That is, M is the midpoint of if M M. 1 What is the definition of an angle bisector?
Geometry Definitions, Postulates, and Theorems. Chapter 4: Congruent Triangles. Section 4.1: Apply Triangle Sum Properties
Geometry efinitions, Postulates, and Theorems Key hapter 4: ongruent Triangles Section 4.1: pply Triangle Sum Properties Standards: 12.0 Students find and use measures of sides and of interior and exterior
5.4. Equilateral and Isosceles Triangles
OMMON OR Learning Standards HSG-O..10 HSG-O..13 HSG-MG..1.4 ONSRUING VIL RGUMNS o be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth
1. Identify the different parts of a triangle 2. Classify triangles by their angle measures 3. Classify triangles by their side lengths
Lesson 8 Lesson 8, page 1 of 6 Glencoe Geometry Chapter 4.1, 4.2 Classifying Triangles & Angle Measure By the end of this lesson, you should be able to 1. Identify the different parts of a triangle 2.
Angles of Triangles. Essential Question How are the angle measures of a triangle related?
2. ngles of Triangles Essential Question How are the angle measures of a triangle related? Writing a onjecture ONSTRUTING VILE RGUMENTS To be proficient in math, you need to reason inductively about data
Name Date. Inscribed Angles and Polygons For use with Exploration arcs? How are the angles of an inscribed quadrilateral related to each other?
Name ate 10.4 Inscribed ngles and Polygons For use with Exploration 10.4 Essential Question How are inscribed angles related to their intercepted arcs? How are the angles of an inscribed quadrilateral
Ch 4 Review Problems pp #7 36, 48,51,52 due MONDAY 12/12
Geometry 4.4 4.6 ongruence Proofs ecember 08, 2016 h 4 Review Problems pp.176 180 #7 36, 48,51,52 due MONY 12/12 h 5 Review Problems pp. 206 209 #15 50 h 6 Review Problems pp. 250 254 #9 19, 33 53 4.2
Ratio of a to b If a and b are two numbers or quantities and b Þ 0, then the ratio of a to b is a }
6.1 Ratios, Proportions, and the Geometric Mean Goal p Solve problems by writing and solving proportions. Your Notes VOULRY Ratio of a to b If a and b are two numbers or quantities and b Þ 0, then the
Whenever two figures have the same size and shape, they are called congruent. Triangles ABC and DEF are congruent. You can match up vertices like
Unit 1: orresponding Parts in a ongruence Section 1: ongruent Figures Whenever two figures have the same size and shape, they are called congruent. F D E Triangles and DEF are congruent. You can match
Properties of Rhombuses, Rectangles, and Squares
6- Properties of Rhombuses, Rectangles, and Squares ontent Standards G.O. Prove theorems about parallelograms... rectangles are parallelograms with congruent diagonals. lso G.SRT.5 Objectives To define
Isosceles and Equilateral Triangles
Locker LESSON 7.2 Isosceles and Equilateral Triangles Texas Math Standards The student is expected to: G.6.D Verify theorems about the relationships in triangles, including... base angles of isosceles
Lesson 1.9.1: Proving the Interior Angle Sum Theorem Warm-Up 1.9.1
NME: SIMILRITY, CONGRUENCE, ND PROOFS Lesson 9: Proving Theorems bout Triangles Lesson 1.9.1: Proving the Interior ngle Sum Theorem Warm-Up 1.9.1 When a beam of light is reflected from a flat surface,
Geometry Unit 4a - Notes Triangle Relationships
Geometry Unit 4a - Notes Triangle Relationships This unit is broken into two parts, 4a & 4b. test should be given following each part. Triangle - a figure formed by three segments joining three noncollinear
H.Geometry Chapter 4 Definition Sheet
Section 4.1 Triangle Sum Theorem The sum of the measure of the angles in a triangle is Conclusions Justification Third Angle Theorem If two angles in one triangle are to two angles in another triangle,
Lesson 3.6 Overlapping Triangles
Lesson 3.6 Overlapping Triangles Getting Ready: Each division in the given triangle is 1 unit long. Hence, the side of the largest triangle is 4- unit long. Figure 3.6.1. Something to think about How many
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
B M. and Quad Quad MNOP
hapter 7 ongruence Postulates &Theorems -Δ s In math, the word congruent is used to describe objects that have the same size and shape. When you traced things when you were a little kid, you were using
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
Lessons 4.1 and 4.2 Triangle Sum Properties & Properties of Isosceles Triangles -Classify triangles and find measures of their angles.
Lessons 4.1 and 4.2 Triangle Sum Properties & Properties of Isosceles Triangles -Classify triangles and find measures of their angles. - Discover the properties of Isosceles Triangles. Classification By
Classify each triangle by its side lengths as equilateral, isosceles, or scalene. (Note: Give two classifications in Exercise 13.)
hapter 4 ongruent Triangles 4.2 and 4.9 lassifying Triangles and Isosceles, and quilateral Triangles. Match the letter of the figure to the correct vocabulary word in xercises 1 4. 1. right triangle 2.
November 21, Angles of Triangles
Geometry Essential Question How are the angle measures of a triangle related? Goals Day 1 Classify triangles by their sides Classify triangles by their angles Identify parts of triangles. Find angle measures
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
4.1 TRIANGLES AND ANGLES
4.1 TRIANGLES AND ANGLES polygon- a closed figure in a plane that is made up of segments, called sides, that intersect only at their endpoints, called vertices Can you name these? triangle- a three-sided
Geometry Notes - Unit 4 Congruence
Geometry Notes - Unit 4 ongruence Triangle is a figure formed by three noncollinear points. lassification of Triangles by Sides Equilateral triangle is a triangle with three congruent sides. Isosceles
Geometry - Concepts 9-12 Congruent Triangles and Special Segments
Geometry - Concepts 9-12 Congruent Triangles and Special Segments Concept 9 Parallel Lines and Triangles (Section 3.5) ANGLE Classifications Acute: Obtuse: Right: SIDE Classifications Scalene: Isosceles:
Angle Relationships in Triangles Focus on Reasoning. Essential question: What are some theorems about angle measures in triangles? G-CO.3.
Name lass 4- Date ngle Relationships in Triangles Focus on Reasoning Essential question: What are some theorems about angle measures in triangles? G-O..0 Investigate the angle measures of a triangle. Use
Theorem (NIB), The "The Adjacent Supplementary Angles" Theorem (Converse of Postulate 14) :
More on Neutral Geometry I (Including Section 3.3) ( "NI" means "NOT IN OOK" ) Theorem (NI), The "The djacent Supplementary ngles" Theorem (onverse of ostulate 14) : If two adjacent angles are supplementary,
1. What is the sum of the measures of the angles in a triangle? Write the proof (Hint: it involves creating a parallel line.)
riangle asics irst: Some basics you should already know. eometry 4.0 1. What is the sum of the measures of the angles in a triangle? Write the proof (Hint: it involves creating a parallel line.) 2. In
Lesson 7.1. Angles of Polygons
Lesson 7.1 Angles of Polygons Essential Question: How can I find the sum of the measures of the interior angles of a polygon? Polygon A plane figure made of three or more segments (sides). Each side intersects
SUGGESTED LEARNING STRATEGIES:
Lesson 22-2 ACTIVITY 22 Learning Targets: Classify angles by their measures. Classify triangles by their angles. Recognize the relationship between the lengths of sides and measures of angles in a triangle.
Explore 2 Exploring Interior Angles in Polygons
Explore 2 Exploring Interior Angles in Polygons To determine the sum of the interior angles for any polygon, you can use what you know about the Triangle Sum Theorem by considering how many triangles there
Mth 97 Winter 2013 Sections 4.3 and 4.4
Section 4.3 Problem Solving Using Triangle Congruence Isosceles Triangles Theorem 4.5 In an isosceles triangle, the angles opposite the congruent sides are congruent. A Given: ABC with AB AC Prove: B C
5.1 Midsegment Theorem and
5.1 Midsegment Theorem and oordinate Proof Georgia Performance Standard(s) MM1G1c, MM1G1e Your Notes Goal p Use properties of midsegments and write coordinate proofs. VOULRY Midsegment of a triangle THEOREM
CHAPTER # 4 CONGRUENT TRIANGLES
HPTER # 4 ONGRUENT TRINGLES In this chapter we address three ig IES: 1) lassify triangles by sides and angles 2) Prove that triangles are congruent 3) Use coordinate geometry to investigate triangle relationships
Math-2. Lesson 7-4 Properties of Parallelograms And Isosceles Triangles
Math-2 Lesson 7-4 Properties of Parallelograms nd Isosceles Triangles What sequence of angles would you link to prove m4 m9 3 1 4 2 13 14 16 15 lternate Interior Corresponding 8 5 7 6 9 10 12 11 What sequence
Identify Points, Lines, and Planes. Undefined term A word without a formal definition
. Identify Points, Lines, and Planes Goal p Name and sketch geometric figures. Your Notes VOULRY Undefined term word without a formal definition Point point has no dimension. It is represented by a dot.
Proving Lines Parallel
Proving Lines Parallel Proving Triangles ongruent 1 Proving Triangles ongruent We know that the opposite sides of a parallelogram are congruent. What about the converse? If we had a quadrilateral whose
Angles of Polygons. b. Draw other polygons and find the sums of the measures of their interior angles. Record your results in the table below.
7.1 TEXS ESSENTIL KNOWLEGE N SKILLS G.5. ngles of Polygons Essential Question What is the sum of the measures of the interior angles of a polygon? of the exterior angles of a polygon? Interior ngle Measures
Ready to Go On? Skills Intervention 4-1 Classifying Triangles
4 Ready to Go On? Skills Intervention 4-1 lassifying Triangles Find these vocabulary words in Lesson 4-1 and the Multilingual Glossary. Vocabulary acute triangle equiangular triangle right triangle obtuse
Geometry Rules! Chapter 4 Notes. Notes #20: Section 4.1 (Congruent Triangles) and Section 4.4 (Isosceles Triangles)
Geometry Rules! hapter 4 Notes Notes #20: Section 4.1 (ongruent Triangles) and Section 4.4 (Isosceles Triangles) ongruent Figures orresponding Sides orresponding ngles *** parts of triangles are *** Practice:
4-1. Congruent Figures. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary. 1. Underline the correct word to complete the sentence.
4-1 ongruent igures Vocabulary Review 1. Underline the correct word to complete the sentence. polygon is a two-dimensional figure with two / three or more segments that meet exactly at their endpoints.
Isosceles and Equilateral Triangles
OMMON ORE Locker LESSON ommon ore Math Standards The student is expected to: OMMON ORE G-O..10 Prove theorems about triangles. Mathematical Practices OMMON ORE 7.2 Isosceles and Equilateral Triangles MP.3
Chapter. Triangles. Copyright Cengage Learning. All rights reserved.
Chapter 3 Triangles Copyright Cengage Learning. All rights reserved. 3.3 Isosceles Triangles Copyright Cengage Learning. All rights reserved. In an isosceles triangle, the two sides of equal length are
Geometry Rules! Chapter 4 Notes. Notes #22: Section 4.1 (Congruent Triangles) and Section 4.5 (Isosceles Triangles)
Name: Geometry Rules! hapter 4 Notes - 1 - Period: Notes #: Section 4.1 (ongruent Triangles) and Section 4.5 (Isosceles Triangles) ongruent Figures orresponding Sides orresponding ngles Triangle ngle-sum
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
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
4-1. Standardized Test Prep. Multiple Choice. Short Response. Congruent Figures. For Exercises 1 6, choose the correct letter.
Name lass ate - tandardized est rep ongruent igures ultiple hoice or xercises, choose the correct letter.. he pair of polygons at the right is congruent. What is m/?. he triangles at the right are congruent.
GEOMETRY Chapter 4 Lesson Plan: Triangle Congruence
GEOMETRY Chapter 4 Lesson Plan: Triangle Congruence Name Per. Chapter 3 Test 4.1 Learning Goal: I can Read through Lesson 4-2 and fill in study classify triangles by using guide. (pgs.223-226) their angle
1/25 Warm Up Find the value of the indicated measure
1/25 Warm Up Find the value of the indicated measure. 1. 2. 3. 4. Lesson 7.1(2 Days) Angles of Polygons Essential Question: What is the sum of the measures of the interior angles of a polygon? What you
Chapter 6.1 Medians. Geometry
Chapter 6.1 Medians Identify medians of triangles Find the midpoint of a line using a compass. A median is a segment that joins a vertex of the triangle and the midpoint of the opposite side. Median AD
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
Warm-Up. Find the domain and range:
Warm-Up Find the domain and range: Geometry Vocabulary & Notation Point Name: Use only the capital letter, without any symbol. Line Name: Use any two points on the line with a line symbol above. AB Line
Reteach. Congruence and Transformations
Congruence and Transformations TYPES OF TRANSFORMATIONS (centered at (0, 0)) Translation (slide): (x, y) (x a, y b) Reflection y-axis: (x, y) ( x, y) x-axis: (x, y) (x, y) Rotation 90 clockwise: (x, y)
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
Geometry Cumulative Study Guide Test 13
Geometry umulative Study Guide Test 13 Numeric Response 1.Find the area, in square feet, of a parallelogram if the height is 9 feet and the base is 4 feet. Name: ate: Period: 10.Find the unknown side lengths
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
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
Type of Triangle Definition Drawing. Name the triangles below, and list the # of congruent sides and angles:
Name: Triangles Test Type of Triangle Definition Drawing Right Obtuse Acute Scalene Isosceles Equilateral Number of congruent angles = Congruent sides are of the congruent angles Name the triangles below,
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
G7-3 Measuring and Drawing Angles and Triangles
G7-3 Measuring and Drawing ngles and Triangles right angle acute angles obtuse angles 90 less than 90 more than 90 and less than 180 1. Without using a protractor, identify each angle as acute or obtuse.
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
Classify Triangles. by the Angle Measure &The Side Lengths. Properties a SCALENE Triangle angles 1.Sum of the interior
Classify s by the Angle Measure &The Side Lengths Foldable Resource & Reference Properties a SCALENE angles 1.Sum of the interior equals. 180 2. The measure of each is side length is. different Note: If
14.2 Angles in Inscribed Quadrilaterals
Name lass ate 14.2 ngles in Inscribed Quadrilaterals Essential Question: What can you conclude about the angles of a quadrilateral inscribed in a circle? Explore G.12. pply theorems about circles, including
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)
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
Stop signs would be examples of congruent shapes. Since a stop sign has 8 sides, they would be congruent octagons.
hapter 5 ongruence Theorems -! s In math, the word congruent is used to describe objects that have the same size and shape. When you traced things when you were a little kid, you were using congruence.
Geometry. Chapter 3. Congruent Triangles Ways of Proving Triangles Corresponding Parts of Δ s (CP Δ=) Theorems Based on Δ s
Geometry hapter 3 ongruent Triangles Ways of Proving Triangles orresponding Parts of Δ s (P Δ=) Theorems ased on Δ s Geometry hapter 3 ongruent Triangles Navigation: lick on sheet number to find that sheet.
Angle Unit Definition Packet
ngle Unit Definition Packet Name lock Date Term Definition Notes Sketch djacent ngles Two angles with a coon, a coon you normay name and, and no coon interior points. 3 4 3 and 4 Vertical ngles Two angles
15.2 Angles in Inscribed Quadrilaterals
Name lass ate 15.2 ngles in Inscribed Quadrilaterals Essential Question: What can you conclude about the angles of a quadrilateral inscribed in a circle? Resource Locker Explore Investigating Inscribed
Unit 4 Day by Day. Day Sections and Objectives Homework. Monday October and 4.9 Packet Pages 1-3
Unit 4 ay by ay ay Sections and Objectives Homework Monday October 26 U41 4.2 and 4.9 Packet Pages 1-3 Types of triangles, isosceles and equilateral triangles Page 228 (23-31, 35-37) Page 288 (5-10, 17-20,
a + b + c = 180 Example: 1. a = 2. b = 3. a = 4.1 Interior angles of a triangle. a = 180 So a = 1 3. Find the missing measurements.
4.1 Interior angles of a triangle. b a a + b + c = 180 c Example: a 70 35 1 3. Find the missing measurements. a + 70 + 35 = 180 So a = 75 1. a = 2. b = a 3 4 6 6 1 4 b 3. a = 135 Triangle Sum onjecture:
Does DEF map to ABC by rigid transformation? because A D C F. (b) List the pairs of congruent angles for the diagram at. right:,, A E.
Name (print first and last) Per Date: 12/17 due 12/19 5.4 ongruence: S and Geometry Regents 2013-2014 Ms. Lomac SLO: I can S and to prove the isosceles triangle theem. (1) Does guarantee that triangles
no triangle can have more than one right angle or obtuse angle.
Congruence Theorems in Action Isosceles Triangle Theorems.3 Learning Goals In this lesson, you will: Prove the Isosceles Triangle Base Theorem. Prove the Isosceles Triangle Vertex Angle Theorem. Prove
Chapter 4. Section 4-1. Classification by Angle. Acute Triangle - a triangle with 3 acute angles!
hapter 4 ongruent Triangles That is water, not cement Section 4-1 lassifying Triangles lassification by ngle cute Triangle - a triangle with 3 acute angles! Equiangular Triangle - a triangle with 3 congruent
Study Guide and Review
Choose the term that best matches the statement or phrase. a square of a whole number A perfect square is a square of a whole number. a triangle with no congruent sides A scalene triangle has no congruent
What could be the name of the plane represented by the top of the box?
hapter 02 Test Name: ate: 1 Use the figure below. What could be the name of the plane represented by the top of the box? E F I 2 Use the figure below. re points,, and E collinear or noncollinear? noncollinear
Objectives. 6-1 Properties and Attributes of Polygons
Objectives Classify polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons. side of a polygon vertex of a polygon diagonal regular polygon concave
Parallel Lines and the Triangle Angle-Sum Theorem. Classify each angle as acute, right, or obtuse
- What You ll Learn To classify triangles and find the measures of their angles To use exterior angles of triangles... nd Why To find the reclining angle of a lounge chair, as in Example Parallel Lines
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
Warm-Up 3/30/ What is the measure of angle ABC.
enchmark #3 Review Warm-Up 3/30/15 1. 2. What is the measure of angle. Warm-Up 3/31/15 1. 2. Five exterior angles of a convex hexagon have measure 74, 84, 42, 13, 26. What is the measure of the 6 th exterior
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
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
5.5 Start Thinking. 5.5 Warm Up. 5.5 Cumulative Review Warm Up. Use a ruler to construct JKL with JK = 1 in., KL = 0.5 in.,
5.5 tart hinking Use a ruler to construct JKL with JK = 1 in., KL = 0.5 in., JL = 1 in. What are the angle measurements in JKL? lassify JKL. onstruct a new triangle, PQ, with JK PQ, KL Q, JL P. re the
Geometry. figure (e.g. multilateral ABCDEF) into the figure A B C D E F is called homothety, or similarity transformation.
ctober 18, 2015 Geometry. Similarity and homothety. Theorems and problems. efinition. Two figures are homothetic with respect to a point, if for each point of one figure there is a corresponding point
Lesson 10: Parts and Types of Triangles
Lesson 10: Parts and Types of Triangles Learning Target: I can find the unknown angles and cite geometric justifications regarding angles in a triangle I can identify different types of triangles based
Skills Practice Skills Practice for Lesson 9.1
Skills Practice Skills Practice for Lesson.1 Name ate Glass Lanterns Introduction to ongruence Vocabulary Identify all parts of the figure that are described by the given term. F E 1. corresponding angles
Name Class Date. Given ABCD QRST, find corresponding parts using the names. Order matters.
Name lass ate Reteaching ongruent igures RS, find corresponding parts using the names. Order matters. or example, RS or example, RS his shows that corresponds to. herefore,. his shows that corresponds
UNIT 5 SIMILARITY AND CONGRUENCE
UNIT 5 SIMILARITY AND CONGRUENCE M2 Ch. 2, 3, 4, 6 and M1 Ch. 13 5.1 Parallel Lines Objective When parallel lines are cut by a transversal, I will be able to identify angle relationships, determine whether
DO NOT LOSE THIS REVIEW! You will not be given another copy.
Geometry Fall Semester Review 2011 Name: O NOT LOS THIS RVIW! You will not be given another copy. The answers will be posted on your teacher s website and on the classroom walls. lso, review the vocabulary
Geo Final Review 2014
Period: ate: Geo Final Review 2014 Multiple hoice Identify the choice that best completes the statement or answers the question. 1. n angle measures 2 degrees more than 3 times its complement. Find the
The angle measure at for example the vertex A is denoted by m A, or m BAC.
MT 200 ourse notes on Geometry 5 2. Triangles and congruence of triangles 2.1. asic measurements. Three distinct lines, a, b and c, no two of which are parallel, form a triangle. That is, they divide the
Skills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name ate onstellations Naming, Measuring, and lassifying ngles Vocabulary Write the term from the box that best completes each statement. point line segment