4.3 Congruent Triangles Quiz
|
|
|
- April Welch
- 7 years ago
- Views:
Transcription
1 Name: Class: Date: ID: A 4.3 Congruent Triangles Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given: ABC MNO Identify all pairs of congruent corresponding parts. a. A M, B N, C O, AB MN, BC NO, AC MO b. A M, B O, C N, AB MN, BC NO, AC MO c. A M, B N, C O, AB MO, BC NO, AC MN d. A O, B N, C M, AB NO, BC MN, AC MO 2. Given that ABC DEC and m E = 23, find m ACB. a. m ACB = 77 b. m ACB = 67 c. m ACB = 23 d. m ACB = 113 1
2 Name: ID: A BONUS 3. Given: RT SU, SRT URT, RS RU. T is the midpoint of SU. Prove: RTS RTU Complete the proof. Proof: Statements Reasons 1. RT SU 1. Given 2. RTS and RTU are right angles. 2. [1] 3. RTS RTU 3. Right Angle Congruence Theorem 4. SRT URT 4. Given 5. S U 5. [2] 6. RS RU 6. Given 7. T is the midpoint of SU. 7. Given 8. ST UT 8. Definition of midpoint 9. RT RT 9. [3] 10. RTS RTU 10. Definition of congruent triangles a. [1] Definition of right angles [3] Transitive Property of Congruence b. [1] Definition of perpendicular lines [3] Reflexive Property of Congruence c. [1] Definition of perpendicular lines [2] Vertical Angles Theorem [3] Symmetric Property of Congruence d. [1] Definition of perpendicular lines [3] Symmetric Property of Congruence 2
![RTS RTU 10. Definition of congruent triangles a. [1] Definition of right angles [3] Transitive Property of Congruence b.](/docs-images/47/20876486/images/page_2.jpg "[1] Definition of perpendicular lines [3] Reflexive Property of Congruence c. [1] Definition of perpendicular lines [2] Vertical Angles Theorem [3] Symmetric Property of Congruence d.")
3 ID: A 4.3 Congruent Triangles Quiz Answer Section MULTIPLE CHOICE 1. ANS: A Corresponding angles and corresponding sides are parts which lie in the same position in the triangles. Corresponding angles: A M, B N, C O Corresponding sides: AB MN, BC NO, AC MO A B C D Correct! The corresponding angles should be in the same position in triangle ABC and triangle MNO. The corresponding sides should be in the same position in triangle ABC and triangle MNO. Check that the corresponding angles and sides are congruent. PTS: 1 DIF: Basic REF: 1a7093be df-9c7d f0d2ea OBJ: Naming Congruent Corresponding Parts NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.C MTH.C TOP: 4-3 Congruent Triangles KEY: correspondence corresponding parts DOK: DOK 1 1
4 ID: A 2. ANS: B m DCE + m CED + m EDC = 180 Triangle Sum Theorem m DCE = 180 Substitution. m DCE = 180 Simplify. m DCE = 67 Subtract 113 from both sides. DCE BCA m DCE = m BCA m ACB = 67 Corresponding parts of congruent triangles are congruent. Definition of congruent angles Corresponding parts of congruent triangles are congruent. A B C D The sum of all angle measures in a triangle is equal to 180 degrees. Correct! Check which angles are corresponding angles. Check your calculations. PTS: 1 DIF: Average REF: 1a72f61a df-9c7d f0d2ea OBJ: Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.G.30 NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C MTH.C TOP: 4-3 Congruent Triangles KEY: triangle sum theorem congruent triangles corresponding parts DOK: DOK 2 2
5 ID: A 3. ANS: B Proof: Statements Reasons 1. RT SU 1. Given 2. RTS and RTU are right angles. 2. Definition of perpendicular lines 3. RTS RTU 3. Right Angle Congruence Theorem 4. SRT URT 4. Given 5. S U 5. Third Angles Theorem 6. RS RU 6. Given 7. T is the midpoint of SU. 7. Given 8. ST UT 8. Definition of midpoint 9. RT RT 9. Reflexive Property of Congruence 10. RTS RTU 10. Definition of congruent triangles A Use the definition of perpendicular lines to show that the lines intersect to form right angles. B Correct! C Angle S and angle U are not vertical angles. Use a different justification for Reason 5. D Use the correct property to show that the part is congruent to itself. PTS: 1 DIF: Average REF: 1a731d2a df-9c7d f0d2ea OBJ: Proving Triangles Congruent NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.PS.4 NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.P MTH.C TOP: 4-3 Congruent Triangles KEY: proof congruent triangles DOK: DOK 1 3
6 Name: Class: Date: ID: B 4.3 Congruent Triangles Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given: ABC MNO Identify all pairs of congruent corresponding parts. a. A M, B O, C N, AB MN, BC NO, AC MO b. A M, B N, C O, AB MN, BC NO, AC MO c. A M, B N, C O, AB MO, BC NO, AC MN d. A O, B N, C M, AB NO, BC MN, AC MO 2. Given that ABC DEC and m E = 23, find m ACB. a. m ACB = 67 b. m ACB = 77 c. m ACB = 23 d. m ACB = 113 1
7 Name: ID: B BONUS 3. Given: RT SU, SRT URT, RS RU. T is the midpoint of SU. Prove: RTS RTU Complete the proof. Proof: Statements Reasons 1. RT SU 1. Given 2. RTS and RTU are right angles. 2. [1] 3. RTS RTU 3. Right Angle Congruence Theorem 4. SRT URT 4. Given 5. S U 5. [2] 6. RS RU 6. Given 7. T is the midpoint of SU. 7. Given 8. ST UT 8. Definition of midpoint 9. RT RT 9. [3] 10. RTS RTU 10. Definition of congruent triangles a. [1] Definition of right angles [3] Transitive Property of Congruence b. [1] Definition of perpendicular lines [3] Reflexive Property of Congruence c. [1] Definition of perpendicular lines [3] Symmetric Property of Congruence d. [1] Definition of perpendicular lines [2] Vertical Angles Theorem [3] Symmetric Property of Congruence 2
![RTS RTU 10. Definition of congruent triangles a. [1] Definition of right angles [3] Transitive Property of Congruence b.](/docs-images/47/20876486/images/page_7.jpg "[1] Definition of perpendicular lines [3] Reflexive Property of Congruence c. [1] Definition of perpendicular lines [3] Symmetric Property of Congruence d.")
8 ID: B 4.3 Congruent Triangles Quiz Answer Section MULTIPLE CHOICE 1. ANS: B Corresponding angles and corresponding sides are parts which lie in the same position in the triangles. Corresponding angles: A M, B N, C O Corresponding sides: AB MN, BC NO, AC MO A B C D The corresponding angles should be in the same position in triangle ABC and triangle MNO. Correct! The corresponding sides should be in the same position in triangle ABC and triangle MNO. Check that the corresponding angles and sides are congruent. PTS: 1 DIF: Basic REF: 1a7093be df-9c7d f0d2ea OBJ: Naming Congruent Corresponding Parts NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.C MTH.C TOP: 4-3 Congruent Triangles KEY: correspondence corresponding parts DOK: DOK 1 1
9 ID: B 2. ANS: A m DCE + m CED + m EDC = 180 Triangle Sum Theorem m DCE = 180 Substitution. m DCE = 180 Simplify. m DCE = 67 Subtract 113 from both sides. DCE BCA m DCE = m BCA m ACB = 67 Corresponding parts of congruent triangles are congruent. Definition of congruent angles Corresponding parts of congruent triangles are congruent. A B C D Correct! The sum of all angle measures in a triangle is equal to 180 degrees. Check which angles are corresponding angles. Check your calculations. PTS: 1 DIF: Average REF: 1a72f61a df-9c7d f0d2ea OBJ: Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.G.30 NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C MTH.C TOP: 4-3 Congruent Triangles KEY: triangle sum theorem congruent triangles corresponding parts DOK: DOK 2 2
10 ID: B 3. ANS: B Proof: Statements Reasons 1. RT SU 1. Given 2. RTS and RTU are right angles. 2. Definition of perpendicular lines 3. RTS RTU 3. Right Angle Congruence Theorem 4. SRT URT 4. Given 5. S U 5. Third Angles Theorem 6. RS RU 6. Given 7. T is the midpoint of SU. 7. Given 8. ST UT 8. Definition of midpoint 9. RT RT 9. Reflexive Property of Congruence 10. RTS RTU 10. Definition of congruent triangles A Use the definition of perpendicular lines to show that the lines intersect to form right angles. B Correct! C Use the correct property to show that the part is congruent to itself. D Angle S and angle U are not vertical angles. Use a different justification for Reason 5. PTS: 1 DIF: Average REF: 1a731d2a df-9c7d f0d2ea OBJ: Proving Triangles Congruent NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.PS.4 NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.P MTH.C TOP: 4-3 Congruent Triangles KEY: proof congruent triangles DOK: DOK 1 3
11 Name: Class: Date: ID: C 4.3 Congruent Triangles Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given: ABC MNO Identify all pairs of congruent corresponding parts. a. A M, B N, C O, AB MN, BC NO, AC MO b. A M, B N, C O, AB MO, BC NO, AC MN c. A O, B N, C M, AB NO, BC MN, AC MO d. A M, B O, C N, AB MN, BC NO, AC MO 2. Given that ABC DEC and m E = 23, find m ACB. a. m ACB = 23 b. m ACB = 67 c. m ACB = 77 d. m ACB = 113 1
12 Name: ID: C BONUS 3. Given: RT SU, SRT URT, RS RU. T is the midpoint of SU. Prove: RTS RTU Complete the proof. Proof: Statements Reasons 1. RT SU 1. Given 2. RTS and RTU are right angles. 2. [1] 3. RTS RTU 3. Right Angle Congruence Theorem 4. SRT URT 4. Given 5. S U 5. [2] 6. RS RU 6. Given 7. T is the midpoint of SU. 7. Given 8. ST UT 8. Definition of midpoint 9. RT RT 9. [3] 10. RTS RTU 10. Definition of congruent triangles a. [1] Definition of perpendicular lines [3] Symmetric Property of Congruence b. [1] Definition of perpendicular lines [3] Reflexive Property of Congruence c. [1] Definition of perpendicular lines [2] Vertical Angles Theorem [3] Symmetric Property of Congruence d. [1] Definition of right angles [3] Transitive Property of Congruence 2
![RTS RTU 10. Definition of congruent triangles a. [1] Definition of perpendicular lines [3] Symmetric Property of Congruence b.](/docs-images/47/20876486/images/page_12.jpg "[1] Definition of perpendicular lines [3] Reflexive Property of Congruence c. [1] Definition of perpendicular lines [2] Vertical Angles Theorem [3] Symmetric Property of Congruence d.")
13 ID: C 4.3 Congruent Triangles Quiz Answer Section MULTIPLE CHOICE 1. ANS: A Corresponding angles and corresponding sides are parts which lie in the same position in the triangles. Corresponding angles: A M, B N, C O Corresponding sides: AB MN, BC NO, AC MO A B C D Correct! The corresponding sides should be in the same position in triangle ABC and triangle MNO. Check that the corresponding angles and sides are congruent. The corresponding angles should be in the same position in triangle ABC and triangle MNO. PTS: 1 DIF: Basic REF: 1a7093be df-9c7d f0d2ea OBJ: Naming Congruent Corresponding Parts NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.C MTH.C TOP: 4-3 Congruent Triangles KEY: correspondence corresponding parts DOK: DOK 1 1
14 ID: C 2. ANS: B m DCE + m CED + m EDC = 180 Triangle Sum Theorem m DCE = 180 Substitution. m DCE = 180 Simplify. m DCE = 67 Subtract 113 from both sides. DCE BCA m DCE = m BCA m ACB = 67 Corresponding parts of congruent triangles are congruent. Definition of congruent angles Corresponding parts of congruent triangles are congruent. A B C D Check which angles are corresponding angles. Correct! The sum of all angle measures in a triangle is equal to 180 degrees. Check your calculations. PTS: 1 DIF: Average REF: 1a72f61a df-9c7d f0d2ea OBJ: Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.G.30 NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C MTH.C TOP: 4-3 Congruent Triangles KEY: triangle sum theorem congruent triangles corresponding parts DOK: DOK 2 2
15 ID: C 3. ANS: B Proof: Statements Reasons 1. RT SU 1. Given 2. RTS and RTU are right angles. 2. Definition of perpendicular lines 3. RTS RTU 3. Right Angle Congruence Theorem 4. SRT URT 4. Given 5. S U 5. Third Angles Theorem 6. RS RU 6. Given 7. T is the midpoint of SU. 7. Given 8. ST UT 8. Definition of midpoint 9. RT RT 9. Reflexive Property of Congruence 10. RTS RTU 10. Definition of congruent triangles A Use the correct property to show that the part is congruent to itself. B Correct! C Angle S and angle U are not vertical angles. Use a different justification for Reason 5. D Use the definition of perpendicular lines to show that the lines intersect to form right angles. PTS: 1 DIF: Average REF: 1a731d2a df-9c7d f0d2ea OBJ: Proving Triangles Congruent NAT: NT.CCSS.MTH G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.PS.4 NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.P MTH.C TOP: 4-3 Congruent Triangles KEY: proof congruent triangles DOK: DOK 1 3
Geometry Module 4 Unit 2 Practice Exam
Name: Class: Date: ID: A Geometry Module 4 Unit 2 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which diagram shows the most useful positioning
Geometry Chapter 2 Study Guide
Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies
Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: lass: _ ate: _ I: SSS Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Given the lengths marked on the figure and that bisects E, use SSS to explain
Geo, Chap 4 Practice Test, EV Ver 1
Class: Date: Geo, Chap 4 Practice Test, EV Ver 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. (4-3) In each pair of triangles, parts are congruent as
POTENTIAL REASONS: Definition of Congruence:
Sec 6 CC Geometry Triangle Pros Name: POTENTIAL REASONS: Definition Congruence: Having the exact same size and shape and there by having the exact same measures. Definition Midpoint: The point that divides
Unit 8: Congruent and Similar Triangles Lesson 8.1 Apply Congruence and Triangles Lesson 4.2 from textbook
Unit 8: Congruent and Similar Triangles Lesson 8.1 Apply Congruence and Triangles Lesson 4.2 from textbook Objectives Identify congruent figures and corresponding parts of closed plane figures. Prove that
[G.CO.2, G.CO.4, G.CO.5]
![[G.CO.2, G.CO.4, G.CO.5]](/thumbs/40/21730129.jpg "[G.CO.2, G.CO.4, G.CO.5]")
Name: Date: Geometric Transformations Multiple Choice Test Bank 1. A triangle has vertices at A (1, 3), B (4, 2), and C (3, 8). Which transformation would produce an image with vertices A (3, 1), B (2,
Algebraic Properties and Proofs
Algebraic Properties and Proofs Name You have solved algebraic equations for a couple years now, but now it is time to justify the steps you have practiced and now take without thinking and acting without
Lesson 13: Angle Sum of a Triangle
Student Outcomes Students know the angle sum theorem for triangles; the sum of the interior angles of a triangle is always 180. Students present informal arguments to draw conclusions about the angle sum
Testing for Congruent Triangles Examples
Testing for Congruent Triangles Examples 1. Why is congruency important? In 1913, Henry Ford began producing automobiles using an assembly line. When products are mass-produced, each piece must be interchangeable,
Exponent Law Review 3 + 3 0. 12 13 b. 1 d. 0. x 5 d. x 11. a 5 b. b 8 a 8. b 2 a 2 d. 81u 8 v 10 81. u 8 v 20 81. Name: Class: Date:
Name: Class: Date: Eponent Law Review Multiple Choice Identify the choice that best completes the statement or answers the question The epression + 0 is equal to 0 Simplify 6 6 8 6 6 6 0 Simplify ( ) (
Vocabulary. Term Page Definition Clarifying Example. biconditional statement. conclusion. conditional statement. conjecture.
CHAPTER Vocabulary The table contains important vocabulary terms from Chapter. As you work through the chapter, fill in the page number, definition, and a clarifying example. biconditional statement conclusion
Mathematics 3301-001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3
Mathematics 3301-001 Spring 2015 Dr. Alexandra Shlapentokh Guide #3 The problems in bold are the problems for Test #3. As before, you are allowed to use statements above and all postulates in the proofs
Triangle Similarity: AA, SSS, SAS Quiz
Name: lass: ate: I: Triangle Similarity:, SSS, SS Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Explain why the triangles are similar and write a
1. A student followed the given steps below to complete a construction. Which type of construction is best represented by the steps given above?
1. A student followed the given steps below to complete a construction. Step 1: Place the compass on one endpoint of the line segment. Step 2: Extend the compass from the chosen endpoint so that the width
Algebra III. Lesson 33. Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids
Algebra III Lesson 33 Quadrilaterals Properties of Parallelograms Types of Parallelograms Conditions for Parallelograms - Trapezoids Quadrilaterals What is a quadrilateral? Quad means? 4 Lateral means?
Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Class: Date: ID: A Q3 Geometry Review Multiple Choice Identify the choice that best completes the statement or answers the question. Graph the image of each figure under a translation by the given
Geometry Regents Review
Name: Class: Date: Geometry Regents Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If MNP VWX and PM is the shortest side of MNP, what is the shortest
Selected practice exam solutions (part 5, item 2) (MAT 360)
Selected practice exam solutions (part 5, item ) (MAT 360) Harder 8,91,9,94(smaller should be replaced by greater )95,103,109,140,160,(178,179,180,181 this is really one problem),188,193,194,195 8. On
Inversion. Chapter 7. 7.1 Constructing The Inverse of a Point: If P is inside the circle of inversion: (See Figure 7.1)
Chapter 7 Inversion Goal: In this chapter we define inversion, give constructions for inverses of points both inside and outside the circle of inversion, and show how inversion could be done using Geometer
Mathematics Geometry Unit 1 (SAMPLE)
Review the Geometry sample year-long scope and sequence associated with this unit plan. Mathematics Possible time frame: Unit 1: Introduction to Geometric Concepts, Construction, and Proof 14 days This
1 Solution of Homework
Math 3181 Dr. Franz Rothe February 4, 2011 Name: 1 Solution of Homework 10 Problem 1.1 (Common tangents of two circles). How many common tangents do two circles have. Informally draw all different cases,
Triangles. Triangle. a. What are other names for triangle ABC?
Triangles Triangle A triangle is a closed figure in a plane consisting of three segments called sides. Any two sides intersect in exactly one point called a vertex. A triangle is named using the capital
Blue Pelican Geometry Theorem Proofs
Blue Pelican Geometry Theorem Proofs Copyright 2013 by Charles E. Cook; Refugio, Tx (All rights reserved) Table of contents Geometry Theorem Proofs The theorems listed here are but a few of the total in
Lecture 24: Saccheri Quadrilaterals
Lecture 24: Saccheri Quadrilaterals 24.1 Saccheri Quadrilaterals Definition In a protractor geometry, we call a quadrilateral ABCD a Saccheri quadrilateral, denoted S ABCD, if A and D are right angles
Incenter and Circumcenter Quiz
Name: lass: ate: I: Incenter and ircumcenter Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. The diagram below shows the construction of the center of
1.1 Identify Points, Lines, and Planes
1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures. Key Vocabulary Undefined terms - These words do not have formal definitions, but there is agreement aboutwhat they mean.
POTENTIAL REASONS: Definition of Congruence: Definition of Midpoint: Definition of Angle Bisector:
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
Chapter 4.1 Parallel Lines and Planes
Chapter 4.1 Parallel Lines and Planes Expand on our definition of parallel lines Introduce the idea of parallel planes. What do we recall about parallel lines? In geometry, we have to be concerned about
GEOMETRY B: CIRCLE TEST PRACTICE
Class: Date: GEOMETRY B: CIRCLE TEST PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the measures of the indicated angles. Which statement
5.1 Midsegment Theorem and Coordinate Proof
5.1 Midsegment Theorem and Coordinate Proof Obj.: Use properties of midsegments and write coordinate proofs. Key Vocabulary Midsegment of a triangle - A midsegment of a triangle is a segment that connects
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 28, 2015 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, January 26, 2016 1:15 to 4:15 p.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, January 26, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The possession or use of any communications
Geometry 8-1 Angles of Polygons
. Sum of Measures of Interior ngles Geometry 8-1 ngles of Polygons 1. Interior angles - The sum of the measures of the angles of each polygon can be found by adding the measures of the angles of a triangle.
Chapter 3.1 Angles. Geometry. Objectives: Define what an angle is. Define the parts of an angle.
Chapter 3.1 Angles Define what an angle is. Define the parts of an angle. Recall our definition for a ray. A ray is a line segment with a definite starting point and extends into infinity in only one direction.
Geometry EOC Practice Test #4
Class: Date: Geometry EOC Practice Test #4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram below, which expression represents x, the degree
Lesson 2: Circles, Chords, Diameters, and Their Relationships
Circles, Chords, Diameters, and Their Relationships Student Outcomes Identify the relationships between the diameters of a circle and other chords of the circle. Lesson Notes Students are asked to construct
Geometry 1. Unit 3: Perpendicular and Parallel Lines
Geometry 1 Unit 3: Perpendicular and Parallel Lines Geometry 1 Unit 3 3.1 Lines and Angles Lines and Angles Parallel Lines Parallel lines are lines that are coplanar and do not intersect. Some examples
/27 Intro to Geometry Review
/27 Intro to Geometry Review 1. An acute has a measure of. 2. A right has a measure of. 3. An obtuse has a measure of. 13. Two supplementary angles are in ratio 11:7. Find the measure of each. 14. In the
DEFINITIONS. 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
Intermediate Math Circles October 10, 2012 Geometry I: Angles
Intermediate Math Circles October 10, 2012 Geometry I: Angles Over the next four weeks, we will look at several geometry topics. Some of the topics may be familiar to you while others, for most of you,
Section 8.8. 1. The given line has equations. x = 3 + t(13 3) = 3 + 10t, y = 2 + t(3 + 2) = 2 + 5t, z = 7 + t( 8 7) = 7 15t.
. The given line has equations Section 8.8 x + t( ) + 0t, y + t( + ) + t, z 7 + t( 8 7) 7 t. The line meets the plane y 0 in the point (x, 0, z), where 0 + t, or t /. The corresponding values for x and
12. Parallels. Then there exists a line through P parallel to l.
12. Parallels Given one rail of a railroad track, is there always a second rail whose (perpendicular) distance from the first rail is exactly the width across the tires of a train, so that the two rails
The Use of Dynamic Geometry Software in the Teaching and Learning of Geometry through Transformations
The Use of Dynamic Geometry Software in the Teaching and Learning of Geometry through Transformations Dynamic geometry technology should be used to maximize student learning in geometry. Such technology
Name: Chapter 4 Guided Notes: Congruent Triangles. Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester
Name: Chapter 4 Guided Notes: Congruent Triangles Chapter Start Date: Chapter End Date: Test Day/Date: Geometry Fall Semester CH. 4 Guided Notes, page 2 4.1 Apply Triangle Sum Properties triangle polygon
A summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs:
summary of definitions, postulates, algebra rules, and theorems that are often used in geometry proofs: efinitions: efinition of mid-point and segment bisector M If a line intersects another line segment
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, January 29, 2014 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, June 20, 2012 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
Solutions Manual for How to Read and Do Proofs
Solutions Manual for How to Read and Do Proofs An Introduction to Mathematical Thought Processes Sixth Edition Daniel Solow Department of Operations Weatherhead School of Management Case Western Reserve
Definitions, Postulates and Theorems
Definitions, s and s Name: Definitions Complementary Angles Two angles whose measures have a sum of 90 o Supplementary Angles Two angles whose measures have a sum of 180 o A statement that can be proven
The common ratio in (ii) is called the scaled-factor. An example of two similar triangles is shown in Figure 47.1. Figure 47.1
47 Similar Triangles An overhead projector forms an image on the screen which has the same shape as the image on the transparency but with the size altered. Two figures that have the same shape but not
TIgeometry.com. Geometry. Angle Bisectors in a Triangle
Angle Bisectors in a Triangle ID: 8892 Time required 40 minutes Topic: Triangles and Their Centers Use inductive reasoning to postulate a relationship between an angle bisector and the arms of the angle.
Section 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18
Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,
Chapter 6 Notes: Circles
Chapter 6 Notes: Circles IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of the circle. Any line segment
Determining Angle Measure with Parallel Lines Examples
Determining Angle Measure with Parallel Lines Examples 1. Using the figure at the right, review with students the following angles: corresponding, alternate interior, alternate exterior and consecutive
The Inversion Transformation
The Inversion Transformation A non-linear transformation The transformations of the Euclidean plane that we have studied so far have all had the property that lines have been mapped to lines. Transformations
Practice Test Answer and Alignment Document Mathematics: Geometry Performance Based Assessment - Paper
The following pages include the answer key for all machine-scored items, followed by the rubrics for the hand-scored items. - The rubrics show sample student responses. Other valid methods for solving
Most popular response to
Class #33 Most popular response to What did the students want to prove? The angle bisectors of a square meet at a point. A square is a convex quadrilateral in which all sides are congruent and all angles
Geometry EOC Practice Test #2
Class: Date: Geometry EOC Practice Test #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Rebecca is loading medical supply boxes into a crate. Each supply
Chapters 6 and 7 Notes: Circles, Locus and Concurrence
Chapters 6 and 7 Notes: Circles, Locus and Concurrence IMPORTANT TERMS AND DEFINITIONS A circle is the set of all points in a plane that are at a fixed distance from a given point known as the center of
Semester Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Are O, N, and P collinear? If so, name the line on which they lie. O N M P a. No,
Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents
Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents Name Chords and Circles: A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.
Quadrilaterals. Definition
Quadrilaterals Definition A quadrilateral is a four-sided closed figure in a plane that meets the following conditions: Each side has its endpoints in common with an endpoint of two adjacent sides. Consecutive
CIRCLE COORDINATE GEOMETRY
CIRCLE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) A circle has equation x + y = 2x + 8 Determine the radius and the coordinates of the centre of the circle. r = 3, ( 1,0 ) Question 2 (**) A circle
Unit Two Practice Test: Powers and Exponent Laws
Class: Date: Unit Two Practice Test: Powers and Exponent Laws Multiple Choice Identify the choice that best completes the statement or answers the question 1 Write the base of ( 6) 5 a 6 b 6 c 6 5 d 5
Lesson 18: Looking More Carefully at Parallel Lines
Student Outcomes Students learn to construct a line parallel to a given line through a point not on that line using a rotation by 180. They learn how to prove the alternate interior angles theorem using
CHAPTER 8 QUADRILATERALS. 8.1 Introduction
CHAPTER 8 QUADRILATERALS 8.1 Introduction You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three non-collinear points in pairs, the figure so obtained is
Grade Level: High School
Lesson I: Triangles- Exterior Angle Theorem KEY WORDS: Triangles, exterior-angle theorem, and remote interior angles. Grade Level: High School SUMMARY: With this investigation students will discover the
Lesson 33: Example 1 (5 minutes)
Student Outcomes Students understand that the Law of Sines can be used to find missing side lengths in a triangle when you know the measures of the angles and one side length. Students understand that
Incenter Circumcenter
TRIANGLE: Centers: Incenter Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle. The radius of incircle is
San Jose Math Circle April 25 - May 2, 2009 ANGLE BISECTORS
San Jose Math Circle April 25 - May 2, 2009 ANGLE BISECTORS Recall that the bisector of an angle is the ray that divides the angle into two congruent angles. The most important results about angle bisectors
Co-ordinate Geometry THE EQUATION OF STRAIGHT LINES
Co-ordinate Geometry THE EQUATION OF STRAIGHT LINES This section refers to the properties of straight lines and curves using rules found by the use of cartesian co-ordinates. The Gradient of a Line. As
Circle Theorems. This circle shown is described an OT. As always, when we introduce a new topic we have to define the things we wish to talk about.
Circle s circle is a set of points in a plane that are a given distance from a given point, called the center. The center is often used to name the circle. T This circle shown is described an OT. s always,
QUADRILATERALS CHAPTER 8. (A) Main Concepts and Results
CHAPTER 8 QUADRILATERALS (A) Main Concepts and Results Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square. Sum of
Heron s Formula. Key Words: Triangle, area, Heron s formula, angle bisectors, incenter
Heron s Formula Lesson Summary: Students will investigate the Heron s formula for finding the area of a triangle. The lab has students find the area using three different methods: Heron s, the basic formula,
Analytical Geometry (4)
Analytical Geometry (4) Learning Outcomes and Assessment Standards Learning Outcome 3: Space, shape and measurement Assessment Standard As 3(c) and AS 3(a) The gradient and inclination of a straight line
Solutions to Practice Problems
Higher Geometry Final Exam Tues Dec 11, 5-7:30 pm Practice Problems (1) Know the following definitions, statements of theorems, properties from the notes: congruent, triangle, quadrilateral, isosceles
Set 4: Special Congruent Triangles Instruction
Instruction Goal: To provide opportunities for students to develop concepts and skills related to proving right, isosceles, and equilateral triangles congruent using real-world problems Common Core Standards
Geometry EOC Practice Test #3
Class: Date: Geometry EOC Practice Test #3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which regular polyhedron has 12 petagonal faces? a. dodecahedron
5-1 Perpendicular and Angle Bisectors
5-1 Perpendicular and Angle Bisectors Equidistant Distance and Perpendicular Bisectors Theorem Hypothesis Conclusion Perpendicular Bisector Theorem Converse of the Perp. Bisector Theorem Locus Applying
Perpendicular and Angle Bisectors Quiz
Name: lass: ate: I: Perpendicular and ngle isectors Quiz Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the measures and. a. = 6.4, = 4.6 b. = 4.6,
Reasoning and Proof Review Questions
www.ck12.org 1 Reasoning and Proof Review Questions Inductive Reasoning from Patterns 1. What is the next term in the pattern: 1, 4, 9, 16, 25, 36, 49...? (a) 81 (b) 64 (c) 121 (d) 56 2. What is the next
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
Name Date Class. Lines and Segments That Intersect Circles. AB and CD are chords. Tangent Circles. Theorem Hypothesis Conclusion
Section. Lines That Intersect Circles Lines and Segments That Intersect Circles A chord is a segment whose endpoints lie on a circle. A secant is a line that intersects a circle at two points. A tangent
Terminology: When one line intersects each of two given lines, we call that line a transversal.
Feb 23 Notes: Definition: Two lines l and m are parallel if they lie in the same plane and do not intersect. Terminology: When one line intersects each of two given lines, we call that line a transversal.
The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach
The Area of a Triangle Using Its Semi-perimeter and the Radius of the In-circle: An Algebraic and Geometric Approach Lesson Summary: This lesson is for more advanced geometry students. In this lesson,
Chapter 5.1 and 5.2 Triangles
Chapter 5.1 and 5.2 Triangles Students will classify triangles. Students will define and use the Angle Sum Theorem. A triangle is formed when three non-collinear points are connected by segments. Each
Session 5 Dissections and Proof
Key Terms for This Session Session 5 Dissections and Proof Previously Introduced midline parallelogram quadrilateral rectangle side-angle-side (SAS) congruence square trapezoid vertex New in This Session
Math 531, Exam 1 Information.
Math 531, Exam 1 Information. 9/21/11, LC 310, 9:05-9:55. Exam 1 will be based on: Sections 1A - 1F. The corresponding assigned homework problems (see http://www.math.sc.edu/ boylan/sccourses/531fa11/531.html)
Exercise Set 3. Similar triangles. Parallel lines
Exercise Set 3. Similar triangles Parallel lines Note: The exercises marked with are more difficult and go beyond the course/examination requirements. (1) Let ABC be a triangle with AB = AC. Let D be an
The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2015 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
3.1 Triangles, Congruence Relations, SAS Hypothesis
Chapter 3 Foundations of Geometry 2 3.1 Triangles, Congruence Relations, SAS Hypothesis Definition 3.1 A triangle is the union of three segments ( called its side), whose end points (called its vertices)
Geometry Handout 2 ~ Page 1
1. Given: a b, b c a c Guidance: Draw a line which intersects with all three lines. 2. Given: a b, c a a. c b b. Given: d b d c 3. Given: a c, b d a. α = β b. Given: e and f bisect angles α and β respectively.
GEOMETRY. Chapter 1: Foundations for Geometry. Name: Teacher: Pd:
GEOMETRY Chapter 1: Foundations for Geometry Name: Teacher: Pd: Table of Contents Lesson 1.1: SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Pgs: 1-4 Lesson 1.2: SWBAT: Use
Class-10 th (X) Mathematics Chapter: Tangents to Circles
Class-10 th (X) Mathematics Chapter: Tangents to Circles 1. Q. AB is line segment of length 24 cm. C is its midpoint. On AB, AC and BC semicircles are described. Find the radius of the circle which touches
Geometry - Semester 2. Mrs. Day-Blattner 1/20/2016
Geometry - Semester 2 Mrs. Day-Blattner 1/20/2016 Agenda 1/20/2016 1) 20 Question Quiz - 20 minutes 2) Jan 15 homework - self-corrections 3) Spot check sheet Thales Theorem - add to your response 4) Finding
Chapter 4: Congruent Triangles
Name: Chapter 4: Congruent Triangles Guided Notes Geometry Fall Semester 4.1 Apply Triangle Sum Properties CH. 4 Guided Notes, page 2 Term Definition Example triangle polygon sides vertices Classifying
Chapter 3. Inversion and Applications to Ptolemy and Euler
Chapter 3. Inversion and Applications to Ptolemy and Euler 2 Power of a point with respect to a circle Let A be a point and C a circle (Figure 1). If A is outside C and T is a point of contact of a tangent
Applications of Fermat s Little Theorem and Congruences
Applications of Fermat s Little Theorem and Congruences Definition: Let m be a positive integer. Then integers a and b are congruent modulo m, denoted by a b mod m, if m (a b). Example: 3 1 mod 2, 6 4
Unit 10 Geometry Circles. NAME Period
Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference