2. In general, dilations do not preserve distance so they are not rigid transformations. Dilations cause the size of the shape to change.
|
|
|
- Moses Ramsey
- 5 years ago
- Views:
Transcription
1 6.1 Dilations 1. To perform a dilation, draw rays starting at the center of dilation through each point. Move each point along the ray according to the scale factor. 2. In general, dilations do not preserve distance so they are not rigid transformations. Dilations cause the size of the shape to change. 3. True 4. The image is larger than the original shape. The distance from the center point to each point has been increased by a factor of Larger 6. Smaller AB = 17 and A B = 68 = The slope of each segment is 1, so the line segments are parallel It does not move. CK-12 Geometry Honors Concepts 1
2 AB = 80 = 4 5 and A B = The slope of each segment is 1, so the line segments are parallel vary. Possible answer: CK-12 Geometry Honors Concepts 2
3 15. vary. Possible answer: 16. The two images are congruent, but in different locations. CK-12 Geometry Honors Concepts 3
4 6.2 Definition of Similarity 1. No. They will only be congruent if the scale factor is Yes. Their corresponding angles will be congruent and their corresponding sides will be proportional with a scale factor of True. Corresponding sides are proportional when triangles are similar. 4. False. AC EF DF BC example, AC DF = BC EF.. This would be correct if one of the fractions was changed to its reciprocal. For 5. True. Corresponding angles are congruent. 6. ΔABC~ΔDEF. Reflect ΔABC across BC. Then dilate the image about point D by a scale factor of The triangles are not similar because the sides are not proportional. AC = 8 BC = 2 while = 5 = 5. DF 4 EF 5 8. ΔABC~ΔFED. The corresponding angles are congruent and the corresponding sides are proportional with a scale factor of ΔABC~ΔEDC. Rotate ΔABC 180 around point C. Dilate about point C with a scale factor of m F = CB = DE = GF = JF = ED = m J = ) Check to see if a similarity transformation would carry one triangle to the other. 2) Check to see if all corresponding angles are congruent and all corresponding sides are proportional. CK-12 Geometry Honors Concepts 4
5 6.3 AA Triangle Similarity 1. AA stands for Angle Angle and it refers to the fact that two triangles are similar if two pairs of corresponding angles are congruent. 2. vary. Triangles should have two pairs of congruent angles. 3. ΔACB~ΔDCF due to the fact that A D and ACB DCF (vertical angles). 4. ΔABC~ΔDBE due to the fact that B B and BED BCA. 5. ΔAEB~ΔCED. Because each triangle is isosceles, its base angles are congruent. Because AEB CED (vertical angles), all four base angles must be congruent. 6. ΔABC~ΔFDE. Note that m B = 30 because the sum of the measures of the interior angles of a triangle is 180. Therefore, there are two pairs of congruent angles. 7. Not enough information. You only have one pair of angles and one pair of sides congruent. 8. Not enough information. You only have one pair of angles congruent. 9. ΔABC ΔFDE by ASA. Note that m E = ΔABC~ΔDEF. Note that m A = ΔAEB~ΔDEC. Parallel lines create congruent alternate interior angles so BAE CDE and ABE DCE. 12. ΔABC~ΔDBE. Parallel lines create congruent corresponding angles so BED BCA and BDE BAC. 13. ΔDBF~ΔDCE. Parallel lines create congruent alternate interior angles so CDB CBF and CDB ECD. This means CBF ECD and gives you two pairs of congruent angles. 14. No, for other shapes you would need more information than just two pairs of angles. 15. Possible answer: You can always dilate the smaller triangle using the ratio between the two given triangles to create a new triangle that is congruent to the original larger triangle by ASA. This means that there will always exist a similarity transformation between the two triangles. CK-12 Geometry Honors Concepts 5
6 6.4 SAS Triangle Similarity 1. SAS stands for side angle side. If two pairs of sides of two triangles are proportional and their included angles are congruent then the triangles are similar. 2. SSA stands for side side angle. This is not a criterion for triangle similarity. 3. vary. 4. vary. 5. ΔAEB~ΔDEC by AA~. Not enough information to use SAS~. 6. Not enough information to know if they are similar. Marked sides and angles are not corresponding. 7. ΔABC~ΔEBD by SAS~. 8. ΔAEB~ΔCED by SAS~. 9. ΔABC~ΔEFD by SAS~. 10. ΔAEB ΔDEC by SAS. 11. You would need to know that AC ED = You would need to know that DE AE = You would need to know that EB = Yes, but they are more than enough information. With AAS or ASA you know two pairs of angles are congruent. This is enough information to show that two triangles are similar by AA~. Therefore, the additional information about the sides would be extra and not necessary. 15. Dilate ΔDEF by a scale factor of AC FD CB (= ). Then, show that the resulting triangle is congruent to DE ΔCBA by SAS. Therefore, a similarity transformation exists between ΔDEF and ΔCBA so the triangles are similar. CK-12 Geometry Honors Concepts 6
7 6.5 SSS Triangle Similarity 1. SSS stands for Side Side Side. If three pairs of sides of two triangles are proportional then the triangles are similar. 2. vary. 3. Neither 4. ΔABC ΔDEF by SSS 5. ΔDEF~ΔABC by SSS~ 6. Not enough information 7. ΔABC~ΔDEF by SSS~ 8. Equilateral triangles are always similar. 9. The ratio of the perimeters is the same as the ratio of the corresponding sides , 20, and , 12, CB = c 2 b 2 and EF = (kc) 2 (kb) 2 = k 2 (c 2 b 2 ) = k c 2 b DF = kc AB c DE = k. = kb AC b EF = k. = k c2 b 2 = k. Because three pairs of sides are proportional, the CB c 2 b 2 triangles are similar by SSS~. This means in general if you have two right triangles and a pair of legs and the hypotenuses are proportional, the triangles are similar. 15. Dilate ΔDEF by a factor of k. The side lengths of ΔD E F will be ka, kb, and kc. ΔD E F ΔACB by SSS. Therefore, a similarity transformation must exist between ΔDEF and ΔACB, so ΔDEF~ΔACB. CK-12 Geometry Honors Concepts 7
8 6.6 Theorems Involving Similarity 1. x = x = 6 3. x = x = x x = x = x = 2 9. z = y = b a = d c b a + 1 = d c + 1 b a + a a = d c + c c b+a a = d+c c 12. ΔYST~ΔYXZ by SAS~ because two pairs of sides are proportional as shown in #11 and their included angles are shared and thus congruent. 13. Because ΔYST~ΔYXZ, corresponding angles are similar. This means YST YXZ. Because corresponding angles are congruent, lines must be parallel. Therefore, ST. XZ 14. Consider the picture from #11 with b = a and d = c. Then, YS = a = 1 YT and = c = 1. Two pairs YX 2a 2 YZ 2c 2 of sides are proportional, and it follows that ST XZ as shown in #12 and # Look at Guided Practice #1-#3 for help. CK-12 Geometry Honors Concepts 8
9 6.7 Applications of Similar Triangles 1. They have two pairs of congruent angles so they are similar by AA~. 2. 1: 3: 2 3. The missing sides are 6 and The missing sides are 8 3 and The missing sides are 8 16 and They have two pairs of congruent angles so they are similar by AA~. 7. 1: 1: 2 8. The missing sides are both length The missing sides are 7 and The missing sides are both Due to parallel lines, CBA DFA and CAB DEB. The triangles are similar by AA~. 12. The scale factor is 2. x = m ADB = 45. ΔADB is an isosceles right triangle. 14. BD = AB = AC 2 = AC = 34. CK-12 Geometry Honors Concepts 9
CP Geometry Quarter 2 Exam
CP Geometry Quarter 2 Exam Geometric Relationships and Properties, Similarity Name: Block: Date: Section Points Earned Points Possible I 60 II 20 III 20 Total 100 I. Multiple Choice 3 points each Identify
For all questions, E. NOTA means none of the above answers is correct. Diagrams are NOT drawn to scale.
For all questions, means none of the above answers is correct. Diagrams are NOT drawn to scale.. In the diagram, given m = 57, m = (x+ ), m = (4x 5). Find the degree measure of the smallest angle. 5. The
Math-2 Lesson 8-6 Unit 5 review -midpoint, -distance, -angles, -Parallel lines, -triangle congruence -triangle similarity -properties of
Math- Lesson 8-6 Unit 5 review -midpoint, -distance, -angles, -Parallel lines, -triangle congruence -triangle similarity -properties of parallelograms -properties of Isosceles triangles The distance between
Math-2A. Lesson 8-3 Triangle Congruence
Math-2A Lesson 8-3 Triangle Congruence Naming Triangles Triangles are named using a small triangle symbol and the three vertices of the triangles. The order of the vertices does not matter for NAMING a
DE to a line parallel to Therefore
Some Proofs 1. In the figure below segment DE cuts across triangle ABC, and CD/CA = CE/CB. Prove that DE is parallel to AB. Consider the dilation with center C and scaling factor CA/CD. This dilation fixes
Math-2. Lesson 5-2. Triangle Congruence
Math-2 Lesson 5-2 Triangle Congruence Naming Triangles Triangles are named using a small triangle symbol and the three vertices of the triangles. The order of the vertices does not matter for NAMING a
1. For each part (a) through (d) below, state which of the three triangles, if any, are similar and why. a.
Exit Ticket Sample Solutions 1. Given ABC and LMN in the diagram below, determine if the triangles are similar. If so, write a similarity statement, and state the criterion used to support your claim.
3. 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
Math-Essentials. Lesson 6-2. Triangle Congruence
Math-Essentials Lesson 6-2 Triangle Congruence Naming Triangles Triangles are named using a small triangle symbol and the three vertices of the triangles. The order of the vertices does not matter for
Essential Question #1 Is it possible to have two right angles as exterior angles of a triangle? Why or why not?
Essential Question #1 Is it possible to have two right angles as exterior angles of a triangle? Why or why not? Triangles are classified into two categories: Triangles Sides Angles Scalene Equilateral
PROVE 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
7 CONGRUENCE OF TRIANGLES
7 CONGRUENCE OF TRIANGLES Exercise 7.1 Q.1. Complete the following statements : (a) Two line segments are congruent if. (b) Among two congruent angles, one has a measure 70 ; the measure of the other angle
Answer Key. 7.1 Forms of Ratios. Chapter 7 Similarity. CK- 12 Basic Geometry Concepts 1. Answers. 1. a) 4: 3. b) 5: 8. c) 6: 19. d) 6: 8: 5 2.
7.1 Forms of Ratios 1. a) 4: 3 b) 5: 8 c) 6: 19 d) 6: 8: 5 2. 1: 1 3. 1: 2 4. 2: 1 5. 1: 1 6. 5: 4: 3 7. 8. 9. 5 12 1 1 19 30 10. 54 and 72 11. 12 and 20 12. 64 and 112 13. 20 14. 240 15. 30 CK- 12 Basic
Math 8 Module 3 End of Module Study Guide
Name ANSWER KEY Date 3/21/14 Lesson 8: Similarity 1. In the picture below, we have a triangle DEF that has been dilated from center O, by scale factor r = ½. The dilated triangle is noted by D E F. We
REVIEW: Find the value of the variable and the measures of all of the angles
Name: Period: Geometry Honors Unit 3: Congruency Homework Section 3.1: Congruent Figures Can you conclude that the triangles are congruent? Justify your answer. 1. ΔGHJ and ΔIHJ 2. ΔQRS and ΔTVS 3. ΔFGH
Proving Theorems about Lines and Angles
Proving Theorems about Lines and Angles Angle Vocabulary Complementary- two angles whose sum is 90 degrees. Supplementary- two angles whose sum is 180 degrees. Congruent angles- two or more angles with
Life is what you make it. Mr. H s dad
Life is what you make it. Mr. H s dad You can classify triangles by if their sides are congruent. Scalene Triangle This triangle has no congruent sides. Isosceles Triangle This triangle has at least 2
Geometry CP. Unit 4 (Congruency of Triangles) Notes
Geometry CP Unit 4 (Congruency of Triangles) Notes S 4.1 Congruent Polygons S Remember from previous lessons that is something is congruent, that it has the same size and same shape. S Another way to look
Name: 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
Chapter 4 part 1. Congruent Triangles
Chapter 4 part 1 Congruent Triangles 4.1 Apply Triangle Sum Properties Objective: Classify triangles and find measures of their angles. Essential Question: How can you find the measure of the third angle
Lesson a: They are congruent by ASA or AAS. b: AC 9.4 units and DF = 20 units
Lesson 7.1.1 7-6. a: They are congruent by ASA or AAS. b: AC 9.4 units and DF = 20 units 7-7. Relationships used will vary, but may include alternate interior angles, Triangle Angle Sum Theorem, etc.;
10) the plane in two different ways Plane M or DCA (3 non-collinear points) Use the figure to name each of the following:
Name: Period Date Pre-AP Geometry Fall 2015 Semester Exam REVIEW *Chapter 1.1 Points Lines Planes Use the figure to name each of the following: 1) three non-collinear points (A, C, B) or (A, C, D) or any
An Approach to Geometry (stolen in part from Moise and Downs: Geometry)
An Approach to Geometry (stolen in part from Moise and Downs: Geometry) Undefined terms: point, line, plane The rules, axioms, theorems, etc. of elementary algebra are assumed as prior knowledge, and apply
Teacher: Mr. Samuels. Name: 1. 2
Teacher: Mr. Samuels Name: 1. 2 As shown in the diagram below of ΔABC, a compass is used to find points D and E, equidistant from point A. Next, the compass is used to find point F, equidistant from points
IMPORTANT VOCABULARY. Scalene Triangle. Triangle. SSS ASA SAS AAS sides/angles
1 Geometry Chapter 5 Test Review Standards/Goals: C.1.f.: I can prove that two triangles are congruent by applying the SSS, SAS, ASA, and AAS congruence statements. C.1.g. I can use the principle that
Geometry Ch 4 Practice Exam
Name: Class: Date: Geometry Ch 4 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If BCDE is congruent to OPQR, then BC is congruent to?.
4. Tierra knows that right angles are congruent. To prove this she would need to use which important axiom below?
Name: Date: The following set of exercises serves to review the important skills and ideas we have developed in this unit. Multiple Choice Practice suur 1. In the following diagram, it is known that ABC
GEOMETRY MIDTERM REVIEW
Name: GEOMETRY MIDTERM REVIEW DATE: Thursday, January 25 th, 2018 at 8:00am ROOM: Please bring in the following: Pens, pencils, compass, ruler & graphing calculator with working batteries (Calhoun will
Unit 8: Similarity Analysis
Name: Geometry Period Unit 8: Similarity Analysis Only 3 Lessons, Practice, and then QUEST In this unit you must bring the following materials with you to class every day: Please note: Calculator Pencil
Proof: Given ABC XYZ, with A X, B Y, and Our strategy is to show C Z and apply ASA. So, WLOG, we assume for contradiction that m C > m Z.
Theorem: AAS Congruence. If under some correspondence, two angles and a side opposite one of the angles of one triangle are congruent, respectively, to the corresponding two angles and side of a second
Similarity and Congruence EOC Assessment (35%)
1. What term is used to describe two rays or two line segments that share a common endpoint? a. Perpendicular Lines b. Angle c. Parallel lines d. Intersection 2. What is a term used to describe two lines
Proving Triangles and Quadrilaterals Satisfy Transformational Definitions
Proving Triangles and Quadrilaterals Satisfy Transformational Definitions 1. Definition of Isosceles Triangle: A triangle with one line of symmetry. a. If a triangle has two equal sides, it is isosceles.
Geometry Review for Semester 1 Final Exam
Name Class Test Date POINTS, LINES & PLANES: Geometry Review for Semester 1 Final Exam Use the diagram at the right for Exercises 1 3. Note that in this diagram ST plane at T. The point S is not contained
Congruence. CK-12 Kaitlyn Spong. Say Thanks to the Authors Click (No sign in required)
Congruence CK-12 Kaitlyn Spong Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit
Triangle Sum Theorem The sum of the measures of the three angles of a triangle is 180º.
Triangle Sum Theorem The sum of the measures of the three angles of a triangle is 180º. Triangle Sum Theorem The sum of the measures of the three angles of a triangle is 180º. No-Choice Theorem If two
Unit 2. Properties of Triangles. Unit Bundle
Unit 2 Properties of Triangles Unit Bundle Math 2 Spring 2017 1 Day Topic Homework Monday 2/6 Triangle Angle Sum Tuesday 2/7 Wednesday 2/8 Thursday 2/9 Friday 2/10 (Early Release) Monday 2/13 Tuesday 2/14
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
Chapter 4 Unit 6 SPRING GEOMETRY Name Hour
CONGRUENT TRIANGLES Chapter 4 Unit 6 SPRING 2019 GEOMETRY Name Hour Geometry Classifying Triangles 4.1 Objectives: Triangles can be classified by their and/or their. 1) classify triangles by their angle
Chapter 4. Triangles and Congruence
Chapter 4 Triangles and Congruence 4.1 Apply Triangle Sum Properties 4.2 Apply Congruence and Triangles 4.3 Prove Triangles Congruent by SSS 4.4 Prove Triangles Congruent by SAS and HL 4.5 Prove Triangles
Unit 3 Congruence & Proofs
Unit 3 Congruence & Proofs Lesson 1: Introduction to Triangle Proofs Opening Exercise Using your knowledge of angle and segment relationships from Unit 1, fill in the following: Definition/Property/Theorem
5.1 Congruent Triangles
5.1 Congruent Triangles Two figures are congruent if they have the same and the same. Definition of Congruent Triangles ΔABC ΔDEF if and only if Corresponding Angles are congruent: Corresponding Sides
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
G-SRT Congruent and Similar
G-SRT Congruent and Similar Triangles Alignments to Content Standards: G-SRT.A.2 Task ABC DEF m( A) = m( D) m( B) = m( E) a. In triangles and below, and. AB = DE Find a sequence of translations, rotations,
Section 4-1 Congruent Figures. Objectives: recognize congruent figures and their corresponding parts
Section 4-1 Congruent Figures Objectives: recognize congruent figures and their corresponding parts Congruent Polygons Congruent Polygons have congruent corresponding parts Congruent sides Congruent Angles
Geometry Vocabulary Word Wall Cards
Geometry Vocabulary Word Wall Cards Mathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development. The cards should
UNIT 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
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
Name Class Date. Find corresponding parts using the order of the letters in the names.
4-1 Reteaching Congruent Figures Given ABCD QRST, find corresponding parts using the names. Order matters. For example, This shows that A corresponds to Q. Therefore, A Q. For example, This shows that
UCS Geometry SEMESTER 1 REVIEW GUIDE #2 STU COPY. 1. Translate the preimage A ( 2, 1) left 4 units and down 7 units.
2015-2016 UCS Geometry SEMESTER 1 REVIEW GUIDE #2 STU COPY 1. Translate the preimage A ( 2, 1) left 4 units and down 7 units. 2. Use the rule (x, y) (x 5, y + 8) to describe in words how the translation
Congruent Polygons and Congruent Parts
Congruent Polygons and Congruent Parts Two polygons are congruent if and only if there is a one-to-one correspondence between their vertices such that corresponding angles are congruent and corresponding
Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1
Name: Class: Date: Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER Multiple Choice. Identify the choice that best completes the statement or answers the question.. Which statement(s) may
3. 4. fraction can not be the length of the third side?
Name: Teacher: Mrs. Ferry 1. 2 In the construction shown below, is drawn. 3. 4 If two sides of a triangle have lengths of and, which fraction can not be the length of the third side? 1. 2. 3. 4. In ABC,
POTENTIAL 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
Day 6: Triangle Congruence, Correspondence and Styles of Proof HOMEWORK
Day 6: Triangle Congruence, Correspondence and Styles of Proof HOMEWORK 1. If AB DE and ABC DEF as shown in the diagram, what additional information would make the triangles congruent using only SAS SAS
Name Date Class Period
Name Date Class Period Activity B 4.6 Comparing Congruent Triangles MATERIALS metric ruler protractor QUESTION EXPLORE 1 If two triangles are congruent what do you know about the corresponding parts of
Chapter 4 Triangles: Congruency & Similarity
1 Chapter 4 Triangles: Congruency & Similarity Concepts & Skills Quilting is a great American pastime especially in the heartland of the United States. Quilts can be simple in nature or as in the photo
G-SRT Similar triangles
G-SRT Similar triangles Alignments to Content Standards: G-SRT.A.3 Task In the two triangles pictured below m( A) = m( D) and m( B) = m( E) : 1 Using a sequence of translations, rotations, reflections,
Unit 5 Triangle Congruence
Unit 5 Triangle Congruence Day Classwork Homework Wednesday 10/25 Unit 4 Test D1 - Proving SAS through Rigid Motions Watch Video Thursday 10/26 Friday 10/27 Monday 10/30 Proving SAS through Rigid Motions
Construction of an Angle bisector
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
Semester 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
Picture: Picture: Picture:
Postulate - Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. Picture: Postulate - Side-Angle-Side (SAS)
Date: Student Name: Teacher Name: Micah Shue. Score:
Analytic Geometry (CCGPS) EOCT Quiz Geometry - (MCC9 12.G.CO.6 ) Rigid Motions, (MCC9 12.G.CO.7 ) Congruence & Rigid Motions, (MCC9 12.G.CO.8 ) Criteria For Triangle Congruence, (MCC9 12.G.CO.9 ) Line
B = the maximum number of unique scalene triangles having all sides of integral lengths and perimeter less than 13
GEOMETRY TEAM #1 A = the m C in parallelogram ABCD with m B= (4x+ 15), m D= (6x+ ) B = the degree measure of the smallest angle in triangle ABC with m A= ( x+ 0), m B= ( x+ 7), m C= (x 15) Find the value
Lesson. Warm Up flowchart proof. 2. False 3. D. Lesson Practice 48. a. assume m X m Y. b. AB is not perpendicular to CB.
Warm Up 1. flowchart proof 2. False 3. D Lesson Practice a. assume m X m Y b. AB is not perpendicular to CB. c. An isosceles triangle has no sides of equal length. d. Assume that a triangle has more than
Geometry CST Questions (2008)
1 Which of the following best describes deductive reasoning? A using logic to draw conclusions based on accepted statements B accepting the meaning of a term without definition C defining mathematical
Geometry First Semester Exam
Class: Date: Geometry First Semester Exam 2013-14 1. T is the midpoint of PQ. Which one of the following is not an appropriate statement? a. PT = TQ c. PT TQ b. PT = TQ d. PT + TQ = PQ 2. Which angle measures
15. K is the midpoint of segment JL, JL = 4x - 2, and JK = 7. Find x, the length of KL, and JL. 8. two lines that do not intersect
Name: Period Date Pre-AP Geometry Fall Semester Exam REVIEW *Chapter 1.1 Points Lines Planes Use the figure to name each of the following: 1. three non-collinear points 2. one line in three different ways
Geometry Cheat Sheet
Geometry Cheat Sheet Chapter 1 Postulate 1-6 Segment Addition Postulate - If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. Postulate 1-7 Angle Addition Postulate -
1) AB CD 2) AB = CD 3) AE = EB 4) CE = DE
1 In trapezoid RSTV with bases RS and VT, diagonals RT and SV intersect at Q. If trapezoid RSTV is not isosceles, which triangle is equal in area to RSV? 1) RQV 2) RST 3) RVT 4) SVT 2 In the diagram below,
Geometry Regular Midterm Exam Review (Chapter 1, 2, 3, 4, 7, 9)
Geometry Regular Midterm Exam Review (Chapter 1, 2, 3, 4, 7, 9) Name: Date: Mod: Use the figure at the right for #1-4 1. What is another name for plane P? A. plane AE B. plane A C. plane BAD D. plane BAC
APEX PON VIDYASHRAM, VELACHERY ( ) HALF-YEARLY WORKSHEET 1 LINES AND ANGLES SECTION A
APEX PON VIDYASHRAM, VELACHERY (2017 18) HALF-YEARLY WORKSHEET 1 CLASS: VII LINES AND ANGLES SECTION A MATHEMATICS 1. The supplement of 0 is. 2. The common end point where two rays meet to form an angle
Geometry Christmas Break
Name: Date: Place all answers for Part. A on a Scantron. 1. In the diagram below, congruent figures 1, 2, and 3 are drawn. 3. Which figure can have the same cross section as a sphere? Which sequence of
HL Maths Junior Certificate Notes by Bronte Smith
HL Maths Junior Certificate Notes by Bronte Smith Paper 1 Number Systems Applied Arithmetic Sets Algebra Functions Factorising 1. Highest Common Factor ab 2a 2 b + 3ab 2 Find the largest factor that can
M2 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.
Chapter 4 UNIT - 1 AXIOMS, POSTULATES AND THEOREMS I. Choose the correct answers: 1. In the figure a pair of alternate angles are
STD-VIII ST. CLARET SCHOOL Subject : MATHEMATICS Chapter 4 UNIT - 1 AXIOMS, POSTULATES AND THEOREMS I. Choose the correct answers: 1. In the figure a pair of alternate angles are a) and b) and c) and d)
Why Can t We Use SSA to Prove Triangles Congruent?
Why Can t We Use SSA to Prove Triangles Congruent? Lesson Summary: When proving triangles congruent by applying the SSS, ASA, and SAS theorems and postulates, students often asked why is there no SSA property.
**If all seven assignments are completed by the day the Mod 12 test is given you will receive 3 extra points on the test. **
Geometry Mod 11 &12 Similarity Section 6.1: I can solve problems by writing and using rates and ratios. I can solve problems by writing and solving proportions. I can use the geometric mean to solve problems.
CP Math 3 Page 1 of 34. Common Core Math 3 Notes - Unit 2 Day 1 Introduction to Proofs. Properties of Congruence. Reflexive. Symmetric If A B, then B
CP Math 3 Page 1 of 34 Common Core Math 3 Notes - Unit 2 Day 1 Introduction to Proofs Properties of Congruence Reflexive A A Symmetric If A B, then B A Transitive If A B and B C then A C Properties of
Similarity Review day 2
Similarity Review day 2 DD, 2.5 ( ΔADB ) A D B Center (, ) Scale Factor = C' C 4 A' 2 A B B' 5 The line y = ½ x 2 is dilated by a scale factor of 2 and centered at the origin. Which equation represents
Honors Geometry Semester Exam Review
Name: Hr: Honors Geometry Semester Exam Review GET ORGANIZED. Successful studying begins with being organized. Bring this packet with you to class every day. DO NOT FALL BEHIND. Do the problems that are
Unit 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
CK-12 Geometry: Similar Polygons
CK-12 Geometry: Similar Polygons Learning Objectives Recognize similar polygons. Identify corresponding angles and sides of similar polygons from a similarity statement. Calculate and apply scale factors.
GEOMETRY. Chapter 4: Triangles. Name: Teacher: Pd:
GEOMETRY Chapter 4: Triangles Name: Teacher: Pd: Table of Contents DAY 1: (Ch. 4-1 & 4-2) Pgs: 1-5 Pgs: 6-7 SWBAT: Classify triangles by their angle measures and side lengths. Use triangle classification
Transformations and Congruence
Name Date Class UNIT 1 Transformations and Congruence Unit Test: C 1. Draw ST. Construct a segment bisector and label the intersection of segments Y. If SY = a + b, what is ST? Explain your reasoning.
Geometry 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
Unit 3 Syllabus: Congruent Triangles
Date Period Unit 3 Syllabus: Congruent Triangles Day Topic 1 4.1 Congruent Figures 4.2 Triangle Congruence SSS and SAS 2 4.3 Triangle Congruence ASA and AAS 3 4.4 Using Congruent Triangles CPCTC 4 Quiz
Similarity. Similar Polygons
Similarity Similar Polygons 1 MAKING CONNECTIONS Dilating a figure produces a figure that is the same as the original figure, but a different. Like motions, dilations preserve measures. Unlike rigid motions,
Situation 1: Congruent Triangles vs. Similar Triangles
Situation 1: Congruent Triangles vs. Similar Triangles Prepared at the University of Georgia EMAT 6500 Date last revised: July 24 th, 2013 Nicolina Scarpelli Prompt: A teacher in a high school Analytic
Use the figure to name each of the following:
Name: Period Date Pre-AP Geometry Fall 2016 Semester Exam REVIEW *Chapter 1.1 Points Lines Planes Use the figure to name each of the following: 1) three non-collinear points 2) one line in three different
Triangles Chapter Problems
Classify the Triangles by Sides or Angles Class Work Triangles Chapter Problems In problems #1-10, choose the most appropriate description for the given triangle. (quilateral, Scalene, Isosceles, Obtuse,
Geometry Practice Questions Semester 1
Geometry Practice Questions Semester 1 MAFS.912.G-CO.1.1 - Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line,
PLANE GEOMETRY SKILL BUILDER ELEVEN
PLANE GEOMETRY SKILL BUILDER ELEVEN Lines, Segments, and Rays The following examples should help you distinguish between lines, segments, and rays. The three undefined terms in geometry are point, line,
The Pythagorean Theorem: For a right triangle, the sum of the two leg lengths squared is equal to the length of the hypotenuse squared.
Math 1 TOOLKITS TOOLKIT: Pythagorean Theorem & Its Converse The Pythagorean Theorem: For a right triangle, the sum of the two leg lengths squared is equal to the length of the hypotenuse squared. a 2 +
G G. eometry nswer Key. eometry. Core Standards. orkbook. orkbook. Common. ommon. dition. ore. tandards. Topical Review Book Company
G G eometr AW nswer Ke eometr C WC orkbook ommon ore orkbook S tandards Common dition E Core Standards Topical Review Book Compan TEST Part I. 2. 9. 2 3. 7. 2 2. 3 2. 6. 3 0. 3. 2 8. 22. 3 3. 7. 2. 2.
There are two ways to name a line. What are the two ways?
Geometry: 1-1 Points, Lines and Planes What are the Undefined Terms? The Undefined Terms are: What is a Point? How is a point named? Example: What is a Line? A line is named two ways. What are the two
Triangles Chapter Problems
Classify the Triangles by Sides or Angles Class Work Triangles Chapter Problems In problems #1-10, choose the most appropriate description for the given triangle. (quilateral, Scalene, Isosceles, Obtuse,
Geometry. 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
Unit 4 Congruent Triangles.notebook. Geometry. Congruent Triangles. AAS Congruence. Review of Triangle Congruence Proofs.
Geometry Congruent Triangles AAS Congruence Review of Triangle Congruence Proofs Return to Table 1 Side opposite Side Side the sides of triangles Adjacent Sides - two sides sharing a common vertex leg
Triangles. 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
Geometry: Unit 3 Congruent Triangles Practice
Notes 1. Read the information in the box below and add the definitions and notation to your tool kit. Then answer the questions below the box. Two figures are CONGRUENT if they have exactly the same size