Study Guide - Geometry
|
|
- Lucinda Hampton
- 5 years ago
- Views:
Transcription
1 Study Guide - Geometry (NOTE: This does not include every topic on the outline. Take other steps to review those.) Page 1: Rigid Motions Page 3: Constructions Page 12: Angle relationships Page 14: Angle Proofs Definitions and Components of Rigid Motions Rigid Motions v taking an object and moving it to a different location without changing its shape or size Translations v shifts an object in an x or/and y direction v Components: - left/right shift - up/down shift v Notation: - T <x,y> tells you how much you move the object to the left or right or/and how much you move it down or up - for example, T <-5,2> would mean a translation of left 5 and up 2, or in other words, you would take each point and change the points to (x-5, y+2) v How to Translate an Object: - once you know how much you will be translating by in the x or/and y direction, change all of the vertices of the shape based on this - for example, if the translation is 4 right and 5 down + point A of a triangle is (2,3), you would translate A so that A would be (6, -2), then do the same thing to the other two points of the triangle v When Trying to Recognize a Translation, Look For: - the image must be congruent - the image must preserve orientation aka the lettering order - the corresponding sides of the pre-image and image are parallel unless they are on the same horizontal or vertical line as the original side Reflections v a flip around an axis of symmetry v How to Reflect a Point on a Graph: - Draw the axis of symmetry given. - Count how many units away that the point is from the axis of symmetry. - Count the same distance going over to the opposite side of the line and label the point. v When Trying to Recognize a Reflection, Look For: - If the pre-image s points are in a clockwise arrangement, the image s points must be in a counterclockwise arrangement. - If the pre-image s points are in a counter-clockwise arrangement, the image s points must be in a clockwise arrangement. Rotations v turns an object around a point v Components:
2 - center of rotation: around what? - angle of rotation: how many degrees? v Notation: - R origin, 90 would mean a rotation of 90 degrees around the origin - R 90 would also mean a rotation of 90 degrees around the origin v How to Rotate an Object: - If the problem tells you to rotate a negative angle, then the object rotates clockwise. - If the problem tells you to rotate a positive angle, then the object rotates counter-clockwise. v When Trying to Recognize a Rotation, Look For: - the letter ordering must be the same A table that is useful: Rotation of 90 : Rotation of 180 : Rotation of 270 :
3 Geometric Constructions (Part 1) Equilateral Triangle: Step 1: Start with line segment AB Step 2: Draw circle A using the radius AB Step 3: Draw circle B with radius AB Step 4: Label one intersection of the two circles Step 5: Draw line segments BC and AC to connect all 3 points All Sides of the triangle are radii of equally sized circles. Equilateral Triangle Inscribed in Circle Step 1: Draw a circle of any radius, label it as circle A Step 2: Choose a point on the border of the circle and label it as B Step 3: Draw circle B using the radius BA Step 4: Label the intersections of the circles as points C and D Step 5: Draw circle D using the radius CD Step 6: Label the intersection between circle D and circle A, E Step 7: Create line segments CD, DE and CE Equilateral Triangle Inscribed In Circle (2 nd Method) Step 1: Draw a circle of any radius, label it as circle A Step 2: Choose a point on the border of the circle and label it as B Step 3: Draw circle B using the radius BA Step 4: Label intersection as C Step 5: Draw circle C with the same radius as circle B Step 6: Label intersection as D Step 7: Repeat the process until you get back to point A Step 8: Connect every other point to get an equilateral triangle
4 Square Inscribed in a Circle Step 1: Draw circle A and mark point B anywhere to be the first vertex of the square Step 2: Draw the diameter with line AB Step 3: Name other intersection as C Step 4: Draw circle B with a radius slightly past A Step 5: Draw circle C with the same radius as circle B Step 6: Label intersections as D and E Step 7: Connect D and E to get line segment DE Step 8: Connect all 4 points to create the square. Hexagon Inscribed in a circle Steps You have to start with the given circle, with a point A in the center. (Or whatever point whey start with) 1. First, you make a point anywhere on the circle. This will be the first vertex. 2. Next, you will set the compass on point A, and set it to its radius. (The side on the circle) name the points as you make them. 3. With radius B, you will have to make an arc across the circle. 4. Next, you will move the compass to the next vertex (point C) and draw another arc. 5. Continue the steps until you have all 6 vertexes. (The length of the hexagon has to be equal to the center of the vertex) 6. Connect the points with a ruler. There should be 6 equal lines. Examples
5 As you can see above, both have 6 equal sides that are inscribed inside of a circle. The first one starts wit point a, and shows the arcs to form the hexagon. Common Mistakes Some mistakes that are normally made when trying to do this construction is not making the points equal. Many people might accidentally change the radius while making the arcs. Another mistake is connecting the points wrong. This can make them unequal swell. When you are constructing a hexagon, all the sides must be equal. Perpendicular bisectors Steps You are going to be given a line segment (AB) 1. First you place your compass on one end of the given line segment. 2. Next, you are going to set the compass to B and create circle BA 3. Then, you are going to set the compass to point A, and create circle AB 4. After you make the two circles, you are going to label the intersection points CD 5. Then you are going to draw the line segment of the two intersections. Examples
6 As you can see in the examples, here there is a line segment going across, and when the two circles you formed intersected, you create the segment. Common mistakes Some common mistakes made when creating this construction is people might create the wrong points for the circles. Another mistake is that people might not evenly crate the bisector, so it might not be even. Constructions: Part 2 - (You saw it coming) Bisecting an Angle: Angles- space between two rays Bisector- the constructed line that divides a segment or angle into two smaller, congruent pieces. 1. Begin with angle A 2. Draw circle A so it intersects both rays (any radius) 3. Label the intersections B and C 4. Draw circle B with radius BC 5. Draw circle C with radius CB 6. Label either intersection X 7. Draw segment AX. AX bisects angle Copying an Angle: 1. Begin with angle A 2. Draw ray EG (put G far away, we re not really going to use G) 3. Draw circle A of any radius and label intersections B and C 4. Draw circle E with radius AC (same radius) and label intersection as F 5. Draw circle F with radius BC 6. Label intersection of two circles as D 7. Draw ray ED A
7 Circumcenter: The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. 1. Start with triangle ABC 2. Draw perpendicular bisector of AB 3. Draw perpendicular bisector of BC 4. Draw perpendicular bisector of AC 5. Label intersection of perpendicular bisectors as O REMEMBER- ***Circumcenter involves the perpendicular bisector, not the angle bisector ***Don t forget to label the intersection of all the perpendicular bisectors, O ***Don t forget to create the circle that touches the triangle at all its vertices Incenter: The Incenter of a triangle is the point where all three angle bisectors always intersect, and is the center of the triangle's incircle. 1. Begin with triangle ABC 2. Draw angle bisector of angle A 3. Draw angle bisector of angle B
8 4. Draw angle bisector of angle C 5. Label intersection of angle bisectors as O REMEMBER- ***Incenter involves the angle bisector, not the perpendicular bisector ***Don t forget to label the intersection of all the angle bisectors, O ***Don t forget to create the circle that is inside the triangle Parallel line through a Point: 1. Begin with segment AB and point C, which is not on segment AB 2. Draw ray AC 3. Draw circle A of any radius, but not past point C. Label the two intersections D and E 4. Draw circle C with radius AD. Label the far intersection as F. 5. Draw circle F with radius DE. 6. The circles from step 4 and step 5 will intersect at two points. Label the bottom point G 7. Draw line CG.
9 REMEMBER- ***Do not pass point C when creating circle A ***The far intersection should be on ray AC ***Think of this as almost copying an angle because you want to create the same line instead of angle, on the point. So you use radius AD and then you use radius DE to create the same angles/lines (If confused by this, just ignore) Constructing an Axis of Symmetry Given Two Reflected Figures: Steps: Reflection- a flip around an axis of symmetry Changes orientation (the arrangement of the vertices in a clockwise vs. Counter-clockwise arrangement) Rigid motion Axis of Symmetry- In a reflection, the axis of symmetry is the perpendicular bisector of every line joining a point to its image 1. Choose any pre-image/image pair, and then connect them with a line. 2. Construct the perpendicular bisector of that line
10 REMEMBER- ***One pair to connect is enough Constructing a Reflected Figure Given an Axis of Symmetry: Reflection- a flip around an axis of symmetry Changes orientation (the arrangement of the vertices in a clockwise vs. Counter-clockwise arrangement) Rigid motion Axis of Symmetry- In a reflection, the axis of symmetry is the perpendicular bisector of every line joining a point to its image Steps- 1. Choose a vertex and construct a circle so it goes through two points on the axis of symmetry 2. Draw the same size circle from each of the two intersections 3. Where the two circles from step 2 intersect is the image 4. Repeat steps 1-3 for all of the other vertices
11 REMEMBER- ***Do all the vertices ***Don t forget to label them(a, B, C ) ***Do one vertice at a time instead of creating all the circle s at once ***Don t let the circle s and point s distract you!
12 Supplementary Angles: angles that have a sum of 180 Common mistakes involving supplementary angles: Often confused with complementary angles (90 ) The angles DO NOT have to be adjacent or congruent Complementary Angles: Angles that have a sum of 90 Common mistakes involving complementary angles: Often confused with supplementary angles (180 ) The angles DO NOT have to be adjacent or congruent Vertical Angles: Angles that are both opposite to one another when two lines cross and are equal Common mistakes involving vertical angles: Straight lines only! If lines are not straight, the angles aren t vertical Do not forget that they are always congruent Alternate Interior Angles: Opposite sides of the line crossing the 2 parallel lines Between the parallel lines Congruent 3 and 6 or 4 and 5 Alternate Exterior Angles: Opposite sides of the transversal Outside of the parallel lines Congruent 1 and 8 or 2 and 7 Corresponding Interior and Exterior Angles: Same side of the transversal
13 Same location Congruent 6 and 2, 5 and 1, 4 and 8, 3 and 7 Tips: Remember that alternate exterior, interior and corresponding angles are always congruent For parallel line proofs: If ( AEA, AIA, CA) are congruent, then the lines are parallel
14 Proof of Angle Relationships Using Statements and Justifications. - You need to know/memorize all the angle relationships. Here are the angle relationships and their definitions: Types of Angle Relationships 1. Supplementary Angles- two angles that form a straight angle. They add up to 180 degrees. 2. Vertical Angles- two angles that are across from each other. Vertical angles are always congruent. 3. Complementary Angles- two angles that form a right angle, which add up to 90 degrees. 4. Corresponding Angles- Two parallel lines are crossed by another line (called the Transversal), the angles in matching corners are called corresponding angles which are always equal. 5. Alternate Interior Angles- two angles inside of the parallel lines that are on different sides of the transversal. they always have the same measure. 6. Alternate Exterior Angles- two angles outside of the parallel lines that are on different sides of the transversal. they always have the same measure. 4, 5, and 6: ALL THREE ANGLES ARE CONGRUENT! - Different types of justifications include: 1. definitions (ex: angles) 2. properties (ex: all are congruent) 3. conditionals (ex: if <something is true>, then <something else is true> - Proving angle congruence requires you to show or explain how two angles equal each other. To do this you need to make a chart. One side of the chart would have your statements and on the opposite side you would write your justifications about the statement you just made. - FOR EXAMPLE: Let s try solving this problem together.
15 Question: What does m equal, and how do you know? Prove it by using a two column chart. How to Solve: Since vertical angle are congruent, we can make 2m+10= 5m- 80. Then we just solve this equation. We can subtract 2m from both sides and add 80 on both sides. This will make the equation 90=3m. Then divide 3 into 90. That will give you a answer of m= 30. Now the first part of the question is done. The next part of the question is very important. The chart you will need to make will look something like this : Of course ours is going to look a little bit different, but
16 you get the idea. First you want to state what s given. In this case that would be that line CD intersects BA. then for the justification you would write given since it s right there for you. Next you would write angle CEA is equal to angle BED. For the justification you would write vertical angles are always congruent. Then the next thing you would write is 2m+10=5m- 80. In this step you are just plugging in the equations give for angle CEA and BED. Last but not least you would solve it and justify it with algebra. Common Mistakes: Many people tend to forget about writing angles. You cannot just state the brief rule. Also, it is important to state that there is a transversal. Important Tips: Look for the angle relationships and use the definition as the justification.
Point A location in geometry. A point has no dimensions without any length, width, or depth. This is represented by a dot and is usually labelled.
Test Date: November 3, 2016 Format: Scored out of 100 points. 8 Multiple Choice (40) / 8 Short Response (60) Topics: Points, Angles, Linear Objects, and Planes Recognizing the steps and procedures for
More informationMAKE GEOMETRIC CONSTRUCTIONS
MAKE GEOMETRIC CONSTRUCTIONS KEY IDEAS 1. To copy a segment, follow the steps given: Given: AB Construct: PQ congruent to AB 1. Use a straightedge to draw a line, l. 2. Choose a point on line l and label
More informationa triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
More informationQuarter 1 Study Guide Honors Geometry
Name: Date: Period: Topic 1: Vocabulary Quarter 1 Study Guide Honors Geometry Date of Quarterly Assessment: Define geometric terms in my own words. 1. For each of the following terms, choose one of the
More informationGeometry Period Unit 2 Constructions Review
Name 2-7 Review Geometry Period Unit 2 Constructions Review Date 2-1 Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties of equilateral
More informationGeometry Period Unit 2 Constructions Review
Name 2-7 Review Geometry Period Unit 2 Constructions Review Date 2-1 Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties of equilateral
More informationMth 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
More informationGeometry Rules. Triangles:
Triangles: Geometry Rules 1. Types of Triangles: By Sides: Scalene - no congruent sides Isosceles - 2 congruent sides Equilateral - 3 congruent sides By Angles: Acute - all acute angles Right - one right
More informationChapter 1-2 Points, Lines, and Planes
Chapter 1-2 Points, Lines, and Planes Undefined Terms: A point has no size but is often represented by a dot and usually named by a capital letter.. A A line extends in two directions without ending. Lines
More informationGeometry Midterm Review 2019
Geometry Midterm Review 2019 Name To prepare for the midterm: Look over past work, including HW, Quizzes, tests, etc Do this packet Unit 0 Pre Requisite Skills I Can: Solve equations including equations
More information14-9 Constructions Review. Geometry Period. Constructions Review
Name Geometry Period 14-9 Constructions Review Date Constructions Review Construct an Inscribed Regular Hexagon and Inscribed equilateral triangle. -Measuring radius distance to make arcs. -Properties
More informationUnit 1: Fundamentals of Geometry
Name: 1 2 Unit 1: Fundamentals of Geometry Vocabulary Slope: m y x 2 2 Formulas- MUST KNOW THESE! y x 1 1 *Used to determine if lines are PARALLEL, PERPENDICULAR, OR NEITHER! Parallel Lines: SAME slopes
More informationGEOMETRY POSTULATES AND THEOREMS. Postulate 1: Through any two points, there is exactly one line.
GEOMETRY POSTULATES AND THEOREMS Postulate 1: Through any two points, there is exactly one line. Postulate 2: The measure of any line segment is a unique positive number. The measure (or length) of AB
More informationStudents are not expected to work formally with properties of dilations until high school.
Domain: Geometry (G) Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software. Standard: 8.G.1. Verify experimentally the properties of rotations, reflections,
More informationIdentify parallel lines, skew lines and perpendicular lines.
Learning Objectives Identify parallel lines, skew lines and perpendicular lines. Parallel Lines and Planes Parallel lines are coplanar (they lie in the same plane) and never intersect. Below is an example
More information3. Given the similarity transformation shown below; identify the composition:
Midterm Multiple Choice Practice 1. Based on the construction below, which statement must be true? 1 1) m ABD m CBD 2 2) m ABD m CBD 3) m ABD m ABC 1 4) m CBD m ABD 2 2. Line segment AB is shown in the
More informationSemester Test Topic Review. Correct Version
Semester Test Topic Review Correct Version List of Questions Questions to answer: What does the perpendicular bisector theorem say? What is true about the slopes of parallel lines? What is true about the
More informationChapter 2: Transformations. Chapter 2 Transformations Page 1
Chapter 2: Transformations Chapter 2 Transformations Page 1 Unit 2: Vocabulary 1) transformation 2) pre-image 3) image 4) map(ping) 5) rigid motion (isometry) 6) orientation 7) line reflection 8) line
More informationExterior Region Interior Region
Lesson 3: Copy and Bisect and Angle Lesson 4: Construct a Perpendicular Bisector Lesson 5: Points of Concurrencies Student Outcomes: ~Students learn how to bisect an angle as well as how to copy an angle
More informationGeometry CP. Unit 1 Notes
Geometry CP Unit 1 Notes 1.1 The Building Blocks of Geometry The three most basic figures of geometry are: Points Shown as dots. No size. Named by capital letters. Are collinear if a single line can contain
More informationGeometry 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 information3 Identify shapes as two-dimensional (lying in a plane, flat ) or three-dimensional ( solid ).
Geometry Kindergarten Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). 1 Describe objects in the environment using names of shapes,
More informationAngles. An angle is: the union of two rays having a common vertex.
Angles An angle is: the union of two rays having a common vertex. Angles can be measured in both degrees and radians. A circle of 360 in radian measure is equal to 2π radians. If you draw a circle with
More informationGeometry: Semester 1 Midterm
Class: Date: Geometry: Semester 1 Midterm Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The first two steps for constructing MNO that is congruent to
More informationConstructions Quiz Review November 29, 2017
Using constructions to copy a segment 1. Mark an endpoint of the new segment 2. Set the point of the compass onto one of the endpoints of the initial line segment 3. djust the compass's width to the other
More information7. 2 More Things Under. Construction. A Develop Understanding Task
7 Construction A Develop Understanding Task Like a rhombus, an equilateral triangle has three congruent sides. Show and describe how you might locate the third vertex point on an equilateral triangle,
More informationGeometry - Chapter 1 - Corrective #1
Class: Date: Geometry - Chapter 1 - Corrective #1 Short Answer 1. Sketch a figure that shows two coplanar lines that do not intersect, but one of the lines is the intersection of two planes. 2. Name two
More informationSegment Addition Postulate: If B is BETWEEN A and C, then AB + BC = AC. If AB + BC = AC, then B is BETWEEN A and C.
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 the point. The DISTANCE between points A and B, written
More information2. A straightedge can create straight line, but can't measure. A ruler can create straight lines and measure distances.
5.1 Copies of Line Segments and Angles Answers 1. A drawing is a rough sketch and a construction is a process to create an exact and accurate geometric figure. 2. A straightedge can create straight line,
More informationedunepal_info
facebook.com/edunepal.info @ edunepal_info Tangent Constructions Session 1 Drawing and designing logos Many symbols are constructed using geometric shapes. The following section explains common geometrical
More information12.4 Rotations. Learning Objectives. Review Queue. Defining Rotations Rotations
12.4. Rotations www.ck12.org 12.4 Rotations Learning Objectives Find the image of a figure in a rotation in a coordinate plane. Recognize that a rotation is an isometry. Review Queue 1. Reflect XY Z with
More informationGeometry Mathematics Content Standards
85 The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical
More informationHUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK
HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE/SUBJECT Geometry A KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS FOUNDATIONS FOR GEOMETRY REASONING PARALLEL &
More informationPOTENTIAL REASONS: Definition of Congruence:
Sec 1.6 CC Geometry Triangle Proofs Name: POTENTIAL REASONS: Definition of Congruence: Having the exact same size and shape and there by having the exact same measures. Definition of Midpoint: The point
More informationGeometry Definitions, Postulates, and Theorems. Chapter 3: Parallel and Perpendicular Lines. Section 3.1: Identify Pairs of Lines and Angles.
Geometry Definitions, Postulates, and Theorems Chapter : Parallel and Perpendicular Lines Section.1: Identify Pairs of Lines and Angles Standards: Prepare for 7.0 Students prove and use theorems involving
More informationChapter 2: Properties of Angles and Triangles
Chapter 2: Properties of Angles and Triangles Section 2.1 Chapter 2: Properties of Angles and Triangles Section 2.1: Angle Properties and Parallel Lines Terminology: Transversal : A line that intersects
More informationCCGPS UNIT 5 Semester 2 COORDINATE ALGEBRA Page 1 of 38. Transformations in the Coordinate Plane
CCGPS UNIT 5 Semester 2 COORDINATE ALGEBRA Page 1 of 38 Transformations in the Coordinate Plane Name: Date: MCC9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line,
More information7. 5 Congruent Triangles to the Rescue
27 7. 5 Congruent Triangles to the Rescue CC BY Anders Sandberg https://flic.kr/p/3gzscg Part 1 A Practice Understanding Task Zac and Sione are exploring isosceles triangles triangles in which two sides
More information2 Formula (given): Volume of a Pyramid V = 1/3 BH What does B represent? Formula: Area of a Trapezoid. 3 Centroid. 4 Midsegment of a triangle
1 Formula: Area of a Trapezoid 2 Formula (given): Volume of a Pyramid V = 1/3 BH What does B represent? 3 Centroid 4 Midsegment of a triangle 5 Slope formula 6 Point Slope Form of Linear Equation *can
More informationNAEP Released Items Aligned to the Iowa Core: Geometry
NAEP Released Items Aligned to the Iowa Core: Geometry Congruence G-CO Experiment with transformations in the plane 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and
More informationUnit 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 informationYou MUST know the big 3 formulas!
Name 3-13 Review Geometry Period Date Unit 3 Lines and angles Review 3-1 Writing equations of lines. Determining slope and y intercept given an equation y = mx + b Writing the equation of a line given
More informationPostulates, 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 informationGeometry. AIR Study Guide
Geometry AIR Study Guide Table of Contents Topic Slide Formulas 3 5 Angles 6 Lines and Slope 7 Transformations 8 Constructions 9 10 Triangles 11 Congruency and Similarity 12 Right Triangles Only 13 Other
More informationUnit 10 Circles 10-1 Properties of Circles Circle - the set of all points equidistant from the center of a circle. Chord - A line segment with
Unit 10 Circles 10-1 Properties of Circles Circle - the set of all points equidistant from the center of a circle. Chord - A line segment with endpoints on the circle. Diameter - A chord which passes through
More informationMADISON ACADEMY GEOMETRY PACING GUIDE
MADISON ACADEMY GEOMETRY PACING GUIDE 2018-2019 Standards (ACT included) ALCOS#1 Know the precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined
More informationGeometry Geometry Grade Grade Grade
Grade Grade Grade 6.G.1 Find the area of right triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the
More informationGeoGebra Workbook 2 More Constructions, Measurements and Sliders
GeoGebra Workbook 2 More Constructions, Measurements and Sliders Paddy Johnson and Tim Brophy www.ul.ie/cemtl/ Table of Contents 1. Square Construction and Measurement 2 2. Circumscribed Circle of a Triangle
More informationUnit 1, Lesson 1: Moving in the Plane
Unit 1, Lesson 1: Moving in the Plane Let s describe ways figures can move in the plane. 1.1: Which One Doesn t Belong: Diagrams Which one doesn t belong? 1.2: Triangle Square Dance m.openup.org/1/8-1-1-2
More informationUnit 6: Connecting Algebra and Geometry Through Coordinates
Unit 6: Connecting Algebra and Geometry Through Coordinates The focus of this unit is to have students analyze and prove geometric properties by applying algebraic concepts and skills on a coordinate plane.
More informationHS Geometry Mathematics CC
Course Description This course involves the integration of logical reasoning and spatial visualization skills. It includes a study of deductive proofs and applications from Algebra, an intense study of
More informationAchievement Level Descriptors Geometry
Achievement Level Descriptors Geometry ALD Stard Level 2 Level 3 Level 4 Level 5 Policy MAFS Students at this level demonstrate a below satisfactory level of success with the challenging Students at this
More informationChapter 2 Similarity and Congruence
Chapter 2 Similarity and Congruence Definitions Definition AB = CD if and only if AB = CD Remember, mab = AB. Definitions Definition AB = CD if and only if AB = CD Remember, mab = AB. Definition ABC =
More informationUNIT 5 GEOMETRY TEMPLATE CREATED BY REGION 1 ESA UNIT 5
UNIT 5 GEOMETRY TEMPLATE CREATED BY REGION 1 ESA UNIT 5 Geometry Unit 5 Overview: Circles With and Without Coordinates In this unit, students prove basic theorems about circles, with particular attention
More informationGeometry. Cluster: Experiment with transformations in the plane. G.CO.1 G.CO.2. Common Core Institute
Geometry Cluster: Experiment with transformations in the plane. G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of
More informationOhio s Learning Standards-Extended. Mathematics. Congruence Standards Complexity a Complexity b Complexity c
Ohio s Learning Standards-Extended Mathematics Congruence Standards Complexity a Complexity b Complexity c Most Complex Least Complex Experiment with transformations in the plane G.CO.1 Know precise definitions
More information, Geometry, Quarter 1
2017.18, Geometry, Quarter 1 The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency 1.
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationMATH 113 Section 8.2: Two-Dimensional Figures
MATH 113 Section 8.2: Two-Dimensional Figures Prof. Jonathan Duncan Walla Walla University Winter Quarter, 2008 Outline 1 Classifying Two-Dimensional Shapes 2 Polygons Triangles Quadrilaterals 3 Other
More informationMadison County Schools Suggested Geometry Pacing Guide,
Madison County Schools Suggested Geometry Pacing Guide, 2016 2017 Domain Abbreviation Congruence G-CO Similarity, Right Triangles, and Trigonometry G-SRT Modeling with Geometry *G-MG Geometric Measurement
More informationGeometry: Traditional Pathway
GEOMETRY: CONGRUENCE G.CO Prove geometric theorems. Focus on validity of underlying reasoning while using variety of ways of writing proofs. G.CO.11 Prove theorems about parallelograms. Theorems include:
More informationBoardworks Ltd KS3 Mathematics. S1 Lines and Angles
1 KS3 Mathematics S1 Lines and Angles 2 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons 3 Lines In Mathematics,
More informationYEC Geometry Scope and Sequence Pacing Guide
YEC Scope and Sequence Pacing Guide Quarter 1st 2nd 3rd 4th Units 1 2 3 4 5 6 7 8 G.CO.1 G.CO.2 G.CO.6 G.CO.9 G.CO.3 G.CO.7 G.CO.10 G.CO.4 G.CO.8 G.CO.11 Congruence G.CO.5 G.CO.12 G.CO.13 Similarity, Right
More informationStandards to Topics. Common Core State Standards 2010 Geometry
Standards to Topics G-CO.01 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 informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS
UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS This unit introduces the concepts of similarity and congruence. The definition of similarity is explored through dilation transformations. The concept of scale
More informationTriangles. Leg = s. Hypotenuse = s 2
Honors Geometry Second Semester Final Review This review is designed to give the student a BASIC outline of what needs to be reviewed for the second semester final exam in Honors Geometry. It is up to
More informationChapter 8. Properties of Triangles and Quadrilaterals. 02/2017 LSowatsky
Chapter 8 Properties of Triangles and Quadrilaterals 02/2017 LSowatsky 1 8-1A: Points, Lines, and Planes I can Identify and label basic geometric figures. LSowatsky 2 Vocabulary: Point: a point has no
More information2. The pentagon shown is regular. Name Geometry Semester 1 Review Guide Hints: (transformation unit)
Name Geometry Semester 1 Review Guide 1 2014-2015 1. Jen and Beth are graphing triangles on this coordinate grid. Beth graphed her triangle as shown. Jen must now graph the reflection of Beth s triangle
More informationConstruction Blueprints A Practice Understanding Task
90 Construction Blueprints A Practice Understanding Task For each of the following straightedge and compass constructions, illustrate or list the steps for completing the construction and give an eplanation
More informationTerm Definition Figure
Notes LT 1.1 - Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do
More informationGeometry Foundations Planning Document
Geometry Foundations Planning Document Unit 1: Chromatic Numbers Unit Overview A variety of topics allows students to begin the year successfully, review basic fundamentals, develop cooperative learning
More informationCommon Core Specifications for Geometry
1 Common Core Specifications for Geometry Examples of how to read the red references: Congruence (G-Co) 2-03 indicates this spec is implemented in Unit 3, Lesson 2. IDT_C indicates that this spec is implemented
More informationPROVE THEOREMS INVOLVING SIMILARITY
PROVE THEOREMS INVOLVING SIMILARITY KEY IDEAS 1. When proving that two triangles are similar, it is sufficient to show that two pairs of corresponding angles of the triangles are congruent. This is called
More information2-1 Transformations and Rigid Motions. ENGAGE 1 ~ Introducing Transformations REFLECT
2-1 Transformations and Rigid Motions Essential question: How do you identify transformations that are rigid motions? ENGAGE 1 ~ Introducing Transformations A transformation is a function that changes
More informationWest Windsor-Plainsboro Regional School District Basic Geometry Grades 9-12
West Windsor-Plainsboro Regional School District Basic Geometry Grades 9-12 Unit 1: Basics of Geometry Content Area: Mathematics Course & Grade Level: Basic Geometry, 9 12 Summary and Rationale This unit
More informationGeometry. Instructional Activities:
GEOMETRY Instructional Activities: Geometry Assessment: A. Direct Instruction A. Quizzes B. Cooperative Learning B. Skill Reviews C. Technology Integration C. Test Prep Questions D. Study Guides D. Chapter
More informationVideos, Constructions, Definitions, Postulates, Theorems, and Properties
Videos, Constructions, Definitions, Postulates, Theorems, and Properties Videos Proof Overview: http://tinyurl.com/riehlproof Modules 9 and 10: http://tinyurl.com/riehlproof2 Module 9 Review: http://tinyurl.com/module9livelesson-recording
More informationChapter 12 Transformations: Shapes in Motion
Chapter 12 Transformations: Shapes in Motion 1 Table of Contents Reflections Day 1.... Pages 1-10 SWBAT: Graph Reflections in the Coordinate Plane HW: Pages #11-15 Translations Day 2....... Pages 16-21
More informationM2 GEOMETRY REVIEW FOR MIDTERM EXAM
M2 GEOMETRY REVIEW FOR MIDTERM EXAM #1-11: True or false? If false, replace the underlined word or phrase to make a true sentence. 1. Two lines are perpendicular if they intersect to form a right angle.
More informationName: Extra Midterm Review January 2018
Name: Extra Midterm Review January 2018 1. Which drawing best illustrates the construction of an equilateral triangle? A) B) C) D) 2. Construct an equilateral triangle in which A is one vertex. A 3. Construct
More informationMake geometric constructions. (Formalize and explain processes)
Standard 5: Geometry Pre-Algebra Plus Algebra Geometry Algebra II Fourth Course Benchmark 1 - Benchmark 1 - Benchmark 1 - Part 3 Draw construct, and describe geometrical figures and describe the relationships
More informationConstruction: Draw a ray with its endpoint on the left. Label this point B.
Name: Ms. Ayinde Date: Geometry CC 1.13: Constructing Angles Objective: To copy angles and construct angle bisectors using a compass and straightedge. To construct an equilateral triangle. Copy an Angle:
More informationCommon Core State Standards High School Geometry Constructions
ommon ore State Standards High School Geometry onstructions HSG.O..12 onstruction: opying a line segment HSG.O..12 onstruction: opying an angle HSG.O..12 onstruction: isecting a line segment HSG.O..12
More informationGEOMETRY BASIC GEOMETRICAL IDEAS. 3) A point has no dimensions (length, breadth or thickness).
CLASS 6 - GEOMETRY BASIC GEOMETRICAL IDEAS Geo means Earth and metron means Measurement. POINT 1) The most basic shape in geometry is the Point. 2) A point determines a location. 3) A point has no dimensions
More information0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 9 8 3 6 2 In the diagram below,. 4 Pentagon PQRST has parallel to. After a translation of, which line
More informationMANHATTAN HUNTER SCIENCE HIGH SCHOOL GEOMETRY CURRICULUM
COORDINATE Geometry Plotting points on the coordinate plane. Using the Distance Formula: Investigate, and apply the Pythagorean Theorem as it relates to the distance formula. (G.GPE.7, 8.G.B.7, 8.G.B.8)
More informationEUCLID S GEOMETRY. Raymond Hoobler. January 27, 2008
EUCLID S GEOMETRY Raymond Hoobler January 27, 2008 Euclid rst codi ed the procedures and results of geometry, and he did such a good job that even today it is hard to improve on his presentation. He lived
More informationno 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
More informationUnit 2: Constructions
Name: Geometry Period Unit 2: Constructions In this unit you must bring the following materials with you to class every day: COMPASS Straightedge (this is a ruler) Pencil This Booklet A device Headphones
More informationVOCABULARY. Chapters 1, 2, 3, 4, 5, 9, and 8. WORD IMAGE DEFINITION An angle with measure between 0 and A triangle with three acute angles.
Acute VOCABULARY Chapters 1, 2, 3, 4, 5, 9, and 8 WORD IMAGE DEFINITION Acute angle An angle with measure between 0 and 90 56 60 70 50 A with three acute. Adjacent Alternate interior Altitude of a Angle
More informationTriangle 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 informationGeometry: Angle Relationships
Geometry: Angle Relationships I. Define the following angles (in degrees) and draw an example of each. 1. Acute 3. Right 2. Obtuse 4. Straight Complementary angles: Supplementary angles: a + b = c + d
More informationGeometry/Pre AP Geometry Common Core Standards
1st Nine Weeks Transformations Transformations *Rotations *Dilation (of figures and lines) *Translation *Flip G.CO.1 Experiment with transformations in the plane. Know precise definitions of angle, circle,
More information4 Triangles and Congruence
www.ck12.org CHAPTER 4 Triangles and Congruence Chapter Outline 4.1 TRIANGLE SUMS 4.2 CONGRUENT FIGURES 4.3 TRIANGLE CONGRUENCE USING SSS AND SAS 4.4 TRIANGLE CONGRUENCE USING ASA, AAS, AND HL 4.5 ISOSCELES
More informationPoints, 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 informationGeometry Topic 2 Lines, Angles, and Triangles
Geometry Topic 2 Lines, Angles, and Triangles MAFS.912.G-CO.3.9 Using the figure below and the fact that line is parallel to segment prove that the sum of the angle measurements in a triangle is 180. Sample
More informationCurriki Geometry Glossary
Curriki Geometry Glossary The following terms are used throughout the Curriki Geometry projects and represent the core vocabulary and concepts that students should know to meet Common Core State Standards.
More informationReview of 7 th Grade Geometry
Review of 7 th Grade Geometry In the 7 th Grade Geometry we have covered: 1. Definition of geometry. Definition of a polygon. Definition of a regular polygon. Definition of a quadrilateral. Types of quadrilaterals
More informationUnit 5: Transformations in the Coordinate Plane
Unit 5: Transformations in the Coordinate Plane In this unit, students review the definitions of three types of transformations that preserve distance and angle: rotations, reflections, and translations.
More informationGrade 9 Math Terminology
Unit 1 Basic Skills Review BEDMAS a way of remembering order of operations: Brackets, Exponents, Division, Multiplication, Addition, Subtraction Collect like terms gather all like terms and simplify as
More information