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Name: ________________________ Class: ___________________ Date: __________ ID: A Geometry - Chapter 4 Review 15-16 Matching Match each vocabulary term with its definition. a. acute triangle b. equilateral triangle c. right triangle d. obtuse triangle e. isosceles triangle f. equiangular triangle g. scalene triangle ____ 1. a triangle with three acute angles ____ 2. a triangle with one obtuse angle ____ 3. a triangle with three congruent sides ____ 4. a triangle with one right angle ____ 5. a triangle with at least two congruent sides Match each vocabulary term with its definition. a. isosceles triangle b. base angle c. scalene triangle d. equiangular triangle e. triangle rigidity f. base g. legs of an isosceles triangle ____ 6. a property of triangles that states that if the side lengths of a triangle are fixed, the triangle can have only one shape ____ 7. a triangle with three congruent angles ____ 8. the side opposite the vertex angle of a triangle ____ 9. one of the two angles that have the base of the triangle as a side ____ 10. one of the two congruent sides of the isosceles triangle 1 Match each vocabulary term with its definition. a. interior angle b. complementary angles c. supplementary angles d. exterior angle e. interior f. remote interior angle g. exterior ____ 11. an angle formed by one side of a polygon and the extension of an adjacent side ____ 12. an angle formed by two sides of a polygon with a common vertex ____ 13. an interior angle of a polygon that is not adjacent to the exterior angle ____ 14. the set of all points outside a polygon ____ 15. the set of all points inside a polygon Match each vocabulary term with its definition. a. exterior angle b. corresponding angles c. interior angle d. included angle e. vertex angle f. included side g. corresponding sides ____ 16. angles in the same relative position in two different polygons that have the same number of angles ____ 17. the angle formed by the legs of a triangle ____ 18. the common side of two consecutive angles of a polygon ____ 19. sides in the same relative position in two different polygons that have the same number of sides ____ 20. the angle formed by two adjacent sides of a polygon Match each vocabulary term with its definition. a. paragraph proof b. two-column proof c. coordinate proof d. auxiliary line e. congruent polygons f. corollary g. CPCTC ____ 21. a style of proof that uses coordinate geometry and algebra ____ 22. two polygons whose corresponding sides and angles are congruent ____ 23. a theorem whose proof follows directly from another theorem 2 ____ 24. an abbreviation for “Corresponding Parts of Congruent Triangles are Congruent,” which can be used as a justification in a proof after two triangles are proven congruent ____ 25. a line drawn in a figure to aid in a proof Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 26. Determine whether triangles a. b. c. d. EFG and The triangles are congruent because (x,y) → (−x,y). The triangles are congruent because (x,y) → (−y,−x). The triangles are congruent because (x,y) → (x,−y). The triangles are congruent because (x,y) → (−y,x). PQR are congruent. EFG can be mapped to PQR by a reflection: EFG can be mapped to PQR by a rotation: EFG can be mapped to PQR by a reflection: EFG can be mapped to PQR by a rotation: 3 ____ 27. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles. Given: AB ≅ ED , BC ≅ DC , AC ≅ EC , ∠A ≅ ∠E Prove: ∆ABC ≅ ∆EDC Complete the proof. Proof: Statements 1. AB ≅ ED , BC ≅ DC , AC ≅ EC 2. ∠A ≅ ∠E 3. ∠BCA ≅ ∠DCE 4. ∠B ≅ ∠D 5. [3] Reasons 1. Given 2. Given 3. [1] 4. [2] 5. Definition of congruent triangles a. c. b. [1] Reflexive Angles Theorem [2] Third Angles Theorem [3] ∆ABC ≅ ∆EDC [1] Third Angles Theorem [2] Vertical Angles Theorem [3] ∠ABC ≅ ∠EDC d. [1] Vertical Angles Theorem [2] Third Angles Theorem [3] ∠ABC ≅ ∠EDC [1] Vertical Angles Theorem [2] Third Angles Theorem [3] ∆ABC ≅ ∆EDC ____ 28. Using the information about John, Jason, and Julie, can you uniquely determine the distances from John to Julie and from Julie to Jason? Explain your answer. Statement 1: John and Jason are standing 12 feet apart. Statement 2: The angle from Julie to John to Jason measures 31°. Statement 3: The angle from John to Jason to Julie measures 49°. a. b. c. d. No. There is no unique configuration. Yes. They form a unique triangle by SAS. Yes. They form a unique triangle by ASA. Yes. They form a unique triangle by SSS. 4 ____ 29. Show ∆ABD ≅ ∆CDB for a = 3. Complete the proof. AB = a + 7 = [1] = 10 CD = 4a − 2 = [2] = 12 − 2 = 10 AD = 6a − 2 = 6(3) − 2 = 18 − 2 = [3] CB = [4] AB ≅ CD. AD ≅ CB. BD ≅ BD by the Reflexive Property of Congruence. So ∆ABD ≅ ∆CDB by [5]. a. [1] a + 7 [2] 4a − 2 [3] 16 [4] 16 [5] SAS c. [1] 3 + 7 [2] 4(3) − 2 [3] 16 [4] 16 [5] SAS b. [1] 3 + 7 [2] 4(3) − 2 [3] 26 [4] 26 [5] SSS d. [1] 3 + 7 [2] 4(3) − 2 [3] 16 [4] 16 [5] SSS Short Answer 30. Classify ∆ABC by its side lengths. 5 31. Two Seyfert galaxies, BW Tauri and M77, represented by points A and B, are equidistant from Earth, represented by point C. What is m∠A? 32. Find the value of x. 33. Find m∠K . 34. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 46°. 6 35. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m∠ACB. 36. ∆ABF ≅ ∆EDG. ∆ABF and ∆GCF are equilateral. AG = 21 and CG = 1 4 AB. Find the total distance from A to B to C to D to E. 37. Write an equation for the line parallel to the line shown that passes through the point (–2, 3). 7 ID: A Geometry - Chapter 4 Review 15-16 Answer Section MATCHING 1. 2. 3. 4. 5. ANS: ANS: ANS: ANS: ANS: A D B C E TOP: TOP: TOP: TOP: TOP: 4-2 Classifying Triangles 4-2 Classifying Triangles 4-2 Classifying Triangles 4-2 Classifying Triangles 4-2 Classifying Triangles 6. 7. 8. 9. 10. ANS: ANS: ANS: ANS: ANS: E D F B G TOP: TOP: TOP: TOP: TOP: 4-5 Triangle Congruence: SSS and SAS 4-2 Classifying Triangles 4-9 Isosceles and Equilateral Triangles 4-9 Isosceles and Equilateral Triangles 4-9 Isosceles and Equilateral Triangles 11. 12. 13. 14. 15. ANS: ANS: ANS: ANS: ANS: D A F G E TOP: TOP: TOP: TOP: TOP: 4-3 Angle Relationships in Triangles 4-3 Angle Relationships in Triangles 4-3 Angle Relationships in Triangles 4-3 Angle Relationships in Triangles 4-3 Angle Relationships in Triangles 16. 17. 18. 19. 20. ANS: ANS: ANS: ANS: ANS: B E F G D TOP: TOP: TOP: TOP: TOP: 4-4 Congruent Triangles 4-9 Isosceles and Equilateral Triangles 4-6 Triangle Congruence: ASA, AAS, and HL 4-4 Congruent Triangles 4-5 Triangle Congruence: SSS and SAS 21. 22. 23. 24. 25. ANS: ANS: ANS: ANS: ANS: C E F G D TOP: TOP: TOP: TOP: TOP: 4-8 Introduction to Coordinate Proof 4-4 Congruent Triangles 4-3 Angle Relationships in Triangles 4-7 Triangle Congruence: CPCTC 4-3 Angle Relationships in Triangles TOP: TOP: TOP: TOP: 4-1 Congruence and Transformations 4-4 Congruent Triangles 4-6 Triangle Congruence: ASA, AAS, and HL 4-5 Triangle Congruence: SSS and SAS MULTIPLE CHOICE 26. 27. 28. 29. ANS: ANS: ANS: ANS: C D C D 1 ID: A SHORT ANSWER 30. ANS: equilateral triangle TOP: 4-2 Classifying Triangles 31. ANS: m∠A = 65° TOP: 4-9 Isosceles and Equilateral Triangles 32. ANS: x=6 TOP: 4-7 Triangle Congruence: CPCTC 33. ANS: m∠K = 63° TOP: 4-3 Angle Relationships in Triangles 34. ANS: m∠DCB = 46° TOP: 4-3 Angle Relationships in Triangles 35. ANS: m∠ACB = 67° TOP: 4-4 Congruent Triangles 36. ANS: 98 TOP: 4-4 Congruent Triangles 37. ANS: y = −3x – 3 TOP: 4-7-Ext. Lines and Slopes 2