Math 3 Review Sheet Ch. 3 November 4, 2011


 Moses Preston
 3 years ago
 Views:
Transcription
1 Math 3 Review Sheet Ch. 3 November 4, 2011 Review Sheet: Not all the problems need to be completed. However, you should look over all of them as they could be similar to test problems. Easy: 1, 3, 9, 10, 12, 13, 17 Medium: 2, 4, 5, 6, 11, 14, 18 Hard: 6, 8, 15, 16 Very Challenging: 7 Tests are made up of mostly medium problems with some easy problems and some hard problems. 1. What additional information is needed to prove these triangles congruent? What postulate would you then use to prove triangles congruent? E F A B C D Solution: If you had AE = CD then you could use SAS. If you had E = C then you could use AAS. If you had BE = CF then you could use HypotenuseLeg. Finally, if you had F = B you could use ASA.
2 2. Prove the following: (You may not use the Isosceles Triangle Theorem or its converse) Given: 1 = 2 A BC = BC Prove: ABC is Isosceles. B 1 2 C Solution: We know 1 = 2 and that BC = BC. Therefore we can prove ABC = ACB by ASA. Then by CPCTC, AB = AC. If a triangle has two congruent legs, it is isosceles; thus ABC is isosceles.
3 3. Prove the following: Given: ADC is isosceles A B is the midpoint of AD B C Prove: ABC = DBC D Solution: It is given that ADC is isosceles, so because isosceles triangles have congruent legs, AC = CD. We are also given that B is the midpoint of AB. Midpoints divide a segment into two congruent segments, so AB = BD. We now have three sets of congruent sides so by SSS ABC = DBC.
4 4. Prove: Given: L is trisected. L F LA is isosceles. Prove: LMF = LOA M F A O Solution: It is given that L is trisected, thus MLF = LF A = LAO because when an angle is trisected it is divide into three congruent parts. It is also given that F LA is isosceles, so because isosceles triangles have congruent legs and base angles, LF = LA and LF A = LAF. Then from the diagram we can say LF M$ LF A and LAO$ LAF. So we can say that LF M = LAO because if two angles are supplementary to congruent angles, then they are congruent. Therefore, by ASA, LMF = LOA.
5 5. Prove: Given: T is the midpoint of MS P Q P MT and QNT are right 1 = 2 R S MR = SN 1 2 Prove: P = Q M T N Solution: It is given that T is the midpoint of MN. So because a midpoint divides a segment into two congruent parts, MT = T N. We also know that 1 = 2 and that P MT and QNT are right. Becuase all right angles are congruent, P MT = QNT. Then RMT is complementary to 1 and SNT is complementary to 2 because they form right angles. So RMT = SNT because if two angles are complementary to congruent angles then they are congruent. It is also given that MR = SN which means we can prove RMT = SNT by SAS. Then by CPCTC ST N = RT M. So we can now show P MT = QNT by ASA. Therefore by CPCTC P = Q.
6 6. Prove: Given: CB = CD A B ABD = EDB C D CB and CD trisect ACE. Prove: ABE = EDC E Solution: It is given that CB = CD and since they are two legs of a triangle, the triangle is isosceles, so CBD is isosceles. Because CBD is isosceles and isosceles triangles have congruent base angles, CBD = DBC. Then it is given that ABD = EDB so by the subtraction property, if you subtract congruent angles into congruent angles, the resulting angles are congruent, ABC = CDE. Now CB and CD trisect ACE, and when an angle is trisected it is divided into three congruent angles, so ACB = BCD = DCE. In conclusion, by ASA we know that ABC = EDC.
7 7. Prove (this one is challenging) Given: AD = DB A B AE = BC F CD = ED E G H C Prove: AF B is isosceles. D Solution: We know AD = DB, AE = BC and CD = ED. Thus, AED = BCD by SSS. Then by CPCTC we can say EDA = CDB. Also, by the reflexive property ADB = ADB so by the addition property in which if you add two congruent angles to the same angle the resulting angles are congruent, ADC = BDE. Then by SAS ADC = BDE. Then by CPCTC DAC = EBD. Because AD = BD, ABD is isosceles because if a triangle has two congruent legs, it is isosceles. Also, if a triangle is isosceles, its base angles are congruent: DAC = DBA. Then by the subtraction property, which says if you subtract congruent angles from congruent angles, the resulting angles are congruent, we have BAF = ABF. Then by the converse of the isosceles triangle theorem, which states that if a triangle has congruent base angles then it is isosceles, we can conclude that BAF is isosceles.
8 8. Prove: Given: AD = CF B E BAC = DF E G ABC = DEF Prove: DGC isosceles A D C F Solution: It is given that BAC = DF E and that ABC = DEF. Then because AD = CF, we can say by the addition property (adding the same segment to congruent segments gives congruent segments) that AC = DF. Then by AAS ABC = F ED. So by CPCTC, GDC = GCD which makes DGC isosceles using the converse of the isosceles triangle theorem.
9 9. Prove: Given: F H bisects GF J and GHJ. G F H Prove: F G = F J J Solution: It is given that F H bisects GF J and GHJ, so because a bisector divides an angle into two congruent parts we can say: 2 = 1 and 3 = 4. Then by the reflexive property F H = F H. So by ASA F GH = F JH. Then by CPCTC F G = F J.
10 10. Prove: Given: 5 = 6 JHG = O GH = MO Prove: J = P J 5 6 G H M P O Solution: We know that 5 = 6. From the diagram we know JGH$ 5 and P MO$ 6. Then because two angles that are supplementary to congruent angles are congruent, we can conclude that JGH = P MO. We are also given that JHG = P OM and GH = MO. So by ASA JGH = P MO. Then by CPCTC J = P.
11 11. Prove: Given: N is comp to NP O N S S is comp to SP R NP O = SP R N = SP Prove: NOP = SRP O P R Solution: It is given that NP O = SP R and that S is comp to SP R and N is comp to N P O. Thus by the complement theorem: if two angles are complementary to congruent angles then they are congruent, N = S. It is also true that N = SP. Therefore by ASA, NOP = SRP.
12 12. Prove: Given: 1 is comp to 3 2 is comp to Prove: 1 = 4 Solution: From the diagram we can see 2 and 3 are vertical angles and because all vertical angles are congruent, 2 = 3. Then we are given 2 is comp to 4 and 1 is comp to 3. Therefore by the complement theorem: if two angles are complementary to congruent angles they are congruent, we can conclude that 1 = 4.
13 13. Prove: Given: P K and JM bisect each other at R. P M R Prove: P J = MK J K Solution: We know that P K and JM bisect each other at R. When a segment is bisected it divides a segment into two congruent parts, thus P R = RK and JR = RM. Also, from the diagram we can conclude that 3 and 4 are vertical angles, and because vertical angles are congruent, 3 = 4. So by SAS P RJ = KRM. Then by CPCTC P J = MK.
14 14. Prove: (Do not use the definition of isosceles or the isosceles triangle theorem) Given: JG is an altitude and a median F F J = HJ. G J Prove: F JG = HJG H Solution: It is given that F J is both a median and an altitude. Because F J is an altitude we can say that F J F H and perpendicular lines imply right angles so F GJ and JGH are right angles. Then JGH = F GJ, because all right angles are congruent. Because F J is a median, it meets F H at its midpoint G. Then F G = GH because a midpoint divides a segment into two congruent segments. And by the reflexive property JG = JG. Therefore by SAS we can conclude F JG = HJG.
15 15. Prove: Given: JK = MK J OP bisects JK and MK O Prove: JO = P K M P K Solution: It is given that JK = MK and that OP bisects JK and MK. When a segment is bisected it is divided in half, so 1JK = JO and 1 MK = MP. Therefore we know 2 2 JO = P K because the division property says like divisions of congruent segments are congruent.
16 16. Prove: Given: HO = MO H M JO = KO HJ is an altitude of HJK O MK is an altitude of MKJ Prove: MKJ = HJK J K Solution: It is given that MK is an altitude of MKJ and HJ is an altitude of HJK. Because altitudes are perpendicular to the side of the triangle they intersect, they form right angles with that side, so HJK and MKJ are right angles. This makes HJK and MKJ right triangles. It is also given that JO = KO and HO = MO. So by the addition property JM = HK. Also, by the reflexive property, JK = JK. Therefore HJK = MKJ by HypotenuseLeg. So by CPCTC, MJK = HJK.
17 17. Prove: Given: ADB = ADC A ABC is isosceles Prove: AD is a median B D C Solution: It is given that ADB = ADC and that ABC is isosceles. Then because isosceles triangles have congruent legs and congruent base angles, B = C and AB = AC. Thus ABD = ACD by AAS. Therefore by CPCTC, BD = DC. So if a point divides a segment into two congruent segments that point is a midpoint, so D is a midpoint. And then we can conclude that AD is a median because it is drawn from the angle of triangle to the midpoint of the opposite side.
18 18. Prove: Given: KG = GJ F G H 2 = 4 1 is comp to 2 3 is comp to 4 F GJ = HGK Prove: F G = HG K J Solution: It is given that F GJ = HGK and we know by the reflexive property that KGJ = KGJ. Thus by the subtraction property F GK = HGJ. It is also given that 2 = 4 and 1 is comp to 2 and 3 is comp to 4. Then we can conclude that 1 = 3 because if two angles are complements of congruent angles then they are congruent. Then KG = GJ so by ASA GF K = GHJ. Then by CPCTC F G = HG.
Properties of Isosceles and Equilateral Triangles
Properties of Isosceles and Equilateral Triangles In an isosceles triangle, the sides and the angles of the triangle are classified by their position in relation to the triangle s congruent sides. Leg
More informationGeometry Problem Solving Drill 08: Congruent Triangles
Geometry Problem Solving Drill 08: Congruent Triangles Question No. 1 of 10 Question 1. The following triangles are congruent. What is the value of x? Question #01 (A) 13.33 (B) 10 (C) 31 (D) 18 You set
More informationLesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31
Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1
More informationTriangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.
Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?
More information1 7.1 Triangle Application Theorems (pg )
Geometry for Enjoyment and Challenge  Text Solutions Ruth Doherty 1 7.1 Triangle Application Theorems (pg.298301) 2. Given: m 1 = 130 m 7 = 70 7 6 5 Prove: Find the measures of 2, 3, 4, 5, 6 4 3 2 1
More informationA plane can be names using a capital cursive letter OR using three points, which are not collinear (not on a straight line)
Geometry  Semester 1 Final Review Quadrilaterals (Including some corrections of typos in the original packet) 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that
More informationTHEOREMS WE KNOW PROJECT
1 This is a list of all of the theorems that you know and that will be helpful when working on proofs for the rest of the unit. In the Notes section I would like you to write anything that will help you
More informationDay 6: Triangle Congruence, Correspondence and Styles of Proof
Name: Day 6: Triangle Congruence, Correspondence and Styles of Proof Date: Geometry CC (M1D) Opening Exercise Given: CE bisects BD Statements 1. bisects 1.Given CE BD Reasons 2. 2. Define congruence in
More informationName: Date: Period: ID: REVIEW CH 1 TEST REVIEW. 1. Sketch and label an example of each statement. b. A B. a. HG. d. M is the midpoint of PQ. c.
Name: Date: Period: ID: REVIEW CH 1 TEST REVIEW 1 Sketch and label an example of each statement a HG b A B c ST UV d M is the midpoint of PQ e Angles 1 and 2 are vertical angles f Angle C is a right angle
More informationProofs Practice Proofs Worksheet #2
Name: No. Per: Date: Serafino Geometry M T W R F 2C Proofs Practice Proofs Worksheet #2 1. Given: O is the midpoint of MN Prove: OW = ON OM = OW 1. O is the midpoint of seg MN Given 2. Segment NO = Segment
More informationGeometry Honors Review for Midterm Exam
Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers
More informationGeometer: CPM Chapters 16 Period: DEAL. 7) Name the transformation(s) that are not isometric. Justify your answer.
Semester 1 Closure Geometer: CPM Chapters 16 Period: DEAL Take time to review the notes we have taken in class so far and previous closure packets. Look for concepts you feel very comfortable with and
More informationBasic Quadrilateral Proofs
Basic Quadrilateral Proofs For each of the following, draw a diagram with labels, create the givens and proof statement to go with your diagram, then write a twocolumn proof. Make sure your work is neat
More informationReview for Geometry Midterm 2015: Chapters 15
Name Period Review for Geometry Midterm 2015: Chapters 15 Short Answer 1. What is the length of AC? 2. Tell whether a triangle can have sides with lengths 1, 2, and 3. 3. Danny and Dana start hiking from
More information2.8 Proving angle relationships cont. ink.notebook. September 20, page 84 page cont. page 86. page 85. Standards. Cont.
2.8 Proving angle relationships cont. ink.notebook page 84 page 83 2.8 cont. page 85 page 86 Lesson Objectives Standards Lesson Notes 2.8 Proving Angle Relationships Cont. Press the tabs to view details.
More information0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?
0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle
More informationEuclidean Geometry Proofs
Euclidean Geometry Proofs History Thales (600 BC) First to turn geometry into a logical discipline. Described as the first Greek philosopher and the father of geometry as a deductive study. Relied on rational
More informationMathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions
Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,
More informationPostulates and Theorems in Proofs
Postulates and Theorems in Proofs A Postulate is a statement whose truth is accepted without proof A Theorem is a statement that is proved by deductive reasoning. The Reflexive Property of Equality: a
More informationTriangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?
Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel
More informationChapter 7. Geometric Inequalities
4. Let m S, then 3 2 m R. Since the angles are supplementary: 3 2580 4568 542 Therefore, m S 42 and m R 38. Part IV 5. Statements Reasons. ABC is not scalene.. Assumption. 2. ABC has at least 2. Definition
More informationGeometry  Semester 1 Final Review Quadrilaterals
Geometry  Semester 1 Final Review Quadrilaterals 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that apply. a. Plane L b. Plane ABC c. Plane DBC d. Plane E e. Plane
More informationGeometry 3 SIMILARITY & CONGRUENCY Congruency: When two figures have same shape and size, then they are said to be congruent figure. The phenomena between these two figures is said to be congruency. CONDITIONS
More information0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?
0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100
More informationright angle an angle whose measure is exactly 90ᴼ
right angle an angle whose measure is exactly 90ᴼ m B = 90ᴼ B two angles that share a common ray A D C B Vertical Angles A D C B E two angles that are opposite of each other and share a common vertex two
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
EOCT Practice Items 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B'
More informationGiven. Segment Addition. Substitution Property of Equality. Division. Subtraction Property of Equality
Mastery Test Questions (10) 1. Question: What is the missing step in the following proof? Given: ABC with DE AC. Prove: Proof: Statement Reason
More information12 Write a twocolumn proof.
Name: Period: Date: ID: A Chapter 4 Review  GH 1 Find each measure. m 1, m 2, m 3 9 Triangles ABC and AFD are vertical congruent equilateral triangles. Find x and y. 2 Determine whether PQR STU given
More informationTRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)
More informationHonors Geometry Review Exercises for the May Exam
Honors Geometry, Spring Exam Review page 1 Honors Geometry Review Exercises for the May Exam C 1. Given: CA CB < 1 < < 3 < 4 3 4 congruent Prove: CAM CBM Proof: 1 A M B 1. < 1 < 1. given. < 1 is supp to
More informationGeometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown.
1. Reflect FOXY across line y = x. 3. Square BERT is transformed to create the image B E R T, as shown. 2. Parallelogram SHAQ is shown. Point E is the midpoint of segment SH. Point F is the midpoint of
More informationWahkiakum School District, PreEOC Geometry 2012
PreEOC Assesment Geometry #1 Wahkiakum School District GEOM Page 1 1. What is the converse of If there are clouds in the sky, then it is raining? 22 A If it is raining, then there are clouds in the sky.
More information41 Classifying Triangles (pp )
Vocabulary acute triangle.............. 216 auxiliary line............... 223 base....................... 273 base angle.................. 273 congruent polygons......... 231 coordinate proof............
More information6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.
6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has
More informationUNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).
1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1). The dilation is Which statement is true? A. B. C. D. AB B' C' A' B' BC AB BC A' B' B' C' AB BC A' B' D'
More information0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationMath 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.
Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the
More informationPostulates, Definitions, and Theorems (Chapter 4)
Postulates, Definitions, and Theorems (Chapter 4) Segment Addition Postulate (SAP) All segments AB and BC have unique real number measures AB and BC such that: ABCBC = AC if and only if B is between A
More informationNozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1Complete 1. in the parallelogram, each two opposite
More informationCONGRUENCE OF TRIANGLES
Congruence of Triangles 11 CONGRUENCE OF TRIANGLES You might have observed that leaves of different trees have different shapes, but leaves of the same tree have almost the same shape. Although they may
More informationName: Class: Date: If AB = 20, BC = 12, and AC = 16, what is the perimeter of trapezoid ABEF?
Class: Date: Analytic Geometry EOC Practice Questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram below of circle O, chords AB and CD
More informationAssignment Assignment for Lesson 6.1
Assignment Assignment for Lesson.1 Name Date Constructing Congruent Triangles or Not Constructing Triangles In each exercise, do the following. a. Use the given information to construct a triangle. b.
More information5. Using a compass and straightedge, construct a bisector of the angle shown below. [Leave all construction marks.]
Name: Regents Review Session Two Date: Common Core Geometry 1. The diagram below shows AB and DE. Which transformation will move AB onto DE such that point D is the image of point A and point E is the
More informationCumulative Test. 101 Holt Geometry. Name Date Class
Choose the best answer. 1. Which of PQ and QR contains P? A PQ only B QR only C Both D Neither. K is between J and L. JK 3x, and KL x 1. If JL 16, what is JK? F 7 H 9 G 8 J 13 3. SU bisects RST. If mrst
More informationAnswer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4.
9.1 Parts of Circles 1. diameter 2. secant 3. chord 4. point of tangency 5. common external tangent 6. common internal tangent 7. the center 8. radius 9. chord 10. The diameter is the longest chord in
More informationHonors Geometry MidTerm Exam Review
Class: Date: Honors Geometry MidTerm Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The
More informationName: Class: Date: 5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28. a. True b.
Indicate whether the statement is true or false. 1. If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square. 2. If M and N are midpoints of sides and of, then. 3. The
More informationNozha Directorate of Education Form : 2 nd Prep
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep Nozha Language Schools Geometry Revision Sheet Ismailia Road Branch Sheet ( 1) 1Complete 1. In the parallelogram, each
More information1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)
More informationWhich statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?
Unit 2 Review 1. Parallelogram FGHJ was translated 3 units down to form parallelogram F 'G'H'J '. Parallelogram F 'G'H'J ' was then rotated 90 counterclockwise about point G' to obtain parallelogram F
More information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
More information0609ge. Geometry Regents Exam AB DE, A D, and B E.
0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible
More informationClass IX Chapter 8 Quadrilaterals Maths
Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer: Let the common ratio between
More information1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3. a cm b cm c cm d. 21.
FALL SEMESTER EXAM REVIEW (Chapters 16) CHAPTER 1 1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3 2. Find the length of PQ. a. 50.9 cm b. 46.3 cm c. 25.7 cm
More informationClass IX Chapter 8 Quadrilaterals Maths
1 Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Let the common ratio between the angles
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 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationGeometry. Midterm Review
Geometry Midterm Review Class: Date: Geometry Midterm Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1 A plumber knows that if you shut off the water
More informationSHW 101 Total: 30 marks
SHW 0 Total: 30 marks 5. 5 PQR 80 (adj. s on st. line) PQR 55 x 55 40 x 85 6. In XYZ, a 90 40 80 a 50 In PXY, b 50 34 84 M+ 7. AB = AD and BC CD AC BD (prop. of isos. ) y 90 BD = ( + ) = AB BD DA x 60
More information1) Exercise 1 In the diagram, ABC = AED, AD = 3, DB = 2 and AE = 2. Determine the length of EC. Solution:
1) Exercise 1 In the diagram, ABC = AED, AD = 3, DB = 2 and AE = 2. Determine the length of EC. Solution: First, we show that AED and ABC are similar. Since DAE = BAC and ABC = AED, we have that AED is
More informationIB MYP Unit 6 Review
Name: Date: 1. Two triangles are congruent if 1. A. corresponding angles are congruent B. corresponding sides and corresponding angles are congruent C. the angles in each triangle have a sum of 180 D.
More informationTriangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR.
Triangles Two geometric figures having the same shape and size are said to be congruent figures. Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.
More informationGeometry  Review for Final Chapters 5 and 6
Class: Date: Geometry  Review for Final Chapters 5 and 6 1. Classify PQR by its sides. Then determine whether it is a right triangle. a. scalene ; right c. scalene ; not right b. isoceles ; not right
More informationGeometry Regents Practice Midterm
Class: Date: Geometry Regents Practice Midterm Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) What is the equation of a line that is parallel
More informationSOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)
1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x
More informationChapter 8: Right Triangles Topic 5: Mean Proportions & Altitude Rules
Name: Date: Do Now: Use the diagram to complete all parts: a) Find all three angles in each triangle. Chapter 8: Right Triangles Topic 5: Mean Proportions & Altitude Rules b) Find side ZY c) Are these
More informationPage 1 of 11 Name: 1) Which figure always has exactly four lines of reflection that map the figure onto itself? A) rectangle B) square C) regular octagon D) equilateral triangle ee4caab3  Page 1 2) In
More informationHonors Geometry Term 1 Practice Final
Name: Class: Date: ID: A Honors Geometry Term 1 Practice Final Short Answer 1. RT has endpoints R Ê Ë Á 4,2 ˆ, T Ê ËÁ 8, 3 ˆ. Find the coordinates of the midpoint, S, of RT. 5. Line p 1 has equation y
More information46 Isosceles and Equilateral Triangles. Refer to the figure. 1. If name two congruent angles. ANSWER: BAC and BCA
Refer to the figure. 1. If name two congruent angles. BAC and BCA 2. If EAC ECA, name two congruent segments. 6. 16 7. PROOF Write a twocolumn proof. Given: is isosceles; bisects ABC. Prove: Find each
More information7. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI.
1. Name three points in the diagram that are not collinear. 2. If RS = 44 and QS = 68, find QR. 3. R, S, and T are collinear. S is between R and T. RS = 2w + 1, ST = w 1, and RT = 18. Use the Segment Addition
More informationChapter 3 Cumulative Review Answers
Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 27, 2011 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More informationGeometry Midterm REVIEW
Name: Class: Date: ID: A Geometry Midterm REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given LM = MP and L, M, and P are not collinear. Draw
More informationChapter 6 Summary 6.1. Using the HypotenuseLeg (HL) Congruence Theorem. Example
Chapter Summary Key Terms corresponding parts of congruent triangles are congruent (CPCTC) (.2) vertex angle of an isosceles triangle (.3) inverse (.4) contrapositive (.4) direct proof (.4) indirect proof
More informationGeometry Honors: Midterm Exam Review January 2018
Name: Period: The midterm will cover Chapters 16. Geometry Honors: Midterm Exam Review January 2018 You WILL NOT receive a formula sheet, but you need to know the following formulas Make sure you memorize
More informationSOLUTIONS TO EXERCISES FOR. MATHEMATICS 133 Part 4. Basic Euclidean concepts and theorems
SOLUTIONS TO EXERCISES FOR MATHEMATICS 133 Part 4 Winter 2009 NOTE ON ILLUSTRATIONS. Drawings for several of the solutions in this file are available in the following file: http://math.ucr.edu/ res/math133/math133solutions04.figures.f13.pdf
More information21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.
21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then
More information2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.
1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 3) Explain why a fourlegged
More informationEOC Review MC Questions
Geometry EOC Review MC Questions Name Date Block You must show all work to receive full credit.  For every 5 answers that are correct, you may receive 5 extra points in the quiz category for a total of
More information2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.
2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem
More informationClass IX Chapter 7 Triangles Maths
Class IX Chapter 7 Triangles Maths 1: Exercise 7.1 Question In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD,
More informationG.CO.69 ONLY COMMON CORE QUESTIONS
Class: Date: G.CO.69 ONLY COMMON CORE QUESTIONS Multiple Choice Identify the choice that best completes the statement or answers the question. 1 The image of ABC after a rotation of 90º clockwise about
More informationtriangles in neutral geometry three theorems of measurement
lesson 10 triangles in neutral geometry three theorems of measurement 112 lesson 10 in this lesson we are going to take our newly created measurement systems, our rulers and our protractors, and see what
More information0612ge. Geometry Regents Exam
0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent
More informationGeometry CP Semester 1 Review Packet. answers_december_2012.pdf
Geometry CP Semester 1 Review Packet Name: *If you lose this packet, you may print off your teacher s webpage. If you can t find it on their webpage, you can find one here: http://www.hfhighschool.org/assets/1/7/sem_1_review_packet
More informationGeometry Practice Midterm
Class: Date: Geometry Practice Midterm 201819 1. If Z is the midpoint of RT, what are x, RZ, and RT? A. x = 19, RZ = 38, and RT = 76 C. x = 17, RZ = 76, and RT = 38 B. x = 17, RZ = 38, and RT = 76 D.
More information0116ge. Geometry Regents Exam RT and SU intersect at O.
Geometry Regents Exam 06 06ge What is the equation of a circle with its center at (5, ) and a radius of 3? ) (x 5) + (y + ) = 3 ) (x 5) + (y + ) = 9 3) (x + 5) + (y ) = 3 4) (x + 5) + (y ) = 9 In the diagram
More informationRhombi, Rectangles and Squares
Rhombi, Rectangles and Squares Math Practice Return to the Table of Contents 1 Three Special Parallelograms All the same properties of a parallelogram apply to the rhombus, rectangle, and square. Rhombus
More informationFill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater
More information0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?
0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30
More information2016 State Mathematics Contest Geometry Test
2016 State Mathematics Contest Geometry Test In each of the following, choose the BEST answer and record your choice on the answer sheet provided. To ensure correct scoring, be sure to make all erasures
More informationQuestion 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD?
Class IX  NCERT Maths Exercise (7.1) Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Solution 1: In ABC and ABD,
More informationProofs. by Bill Hanlon
Proofs by Bill Hanlon Future Reference To prove congruence, it is important that you remember not only your congruence theorems, but know your parallel line theorems, and theorems concerning triangles.
More informationGrade 7 Lines and Angles
ID : ae7linesandangles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If lines AC and BD intersects at point O such that AOB: BOC = 3:2, f ind
More informationPractice Test Student Answer Document
Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
More informationUnit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity
Unit 5, Lesson 4.3 Proving the Pythagorean Theorem using Similarity Geometry includes many definitions and statements. Once a statement has been shown to be true, it is called a theorem. Theorems, like
More informationClass IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).
Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD, AC = AD (Given) CAB = DAB (AB bisects
More information2/11/16 Review for Proofs Quiz
2/11/16 Review for Proofs Quiz EQ:Name some of the most common properties, theorems, and postulates used when performing proofs. MCC9 12.G.CO.9 Prove theorems about lines and angles. Theorems include:
More informationMidpoint M of points (x1, y1) and (x2, y2) = 1 2
Geometry Semester 1 Exam Study Guide Name Date Block Preparing for the Semester Exam Use notes, homework, checkpoints, quizzes, and tests to prepare. If you lost any of the notes, reprint them from my
More informationHonors Geometry Semester Review Packet
Honors Geometry Semester Review Packet 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear
More information1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?
1 For all problems, NOTA stands for None of the Above. 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? (A) 40 (B) 60 (C) 80 (D) Cannot be determined
More information