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Review 4 Multiple Choice Identify the choice that best completes the statement or answers the question. Use a protractor to classify the triangle as acute, a. obtuse equiangular, obtuse, or right. b. right c. equiangular and obtuse d. equiangular and acute 1. Find the measures of the sides of and classify the triangle by its sides. 2. a. equilateral c. scalene b. isosceles d. obtuse Find each measure. a. b. 3. c. d. 2 59° 47° 1 3 64° 4. 41° 47° 2 1 66° 3 37° a. c. b. d. 5. 45° 43° 2 39° 1 3 a. c. b. d. 6. 55° 2 3 28° 1 46° a. c. b. d. Name the congruent angles and sides for the pair of congruent triangles. 7. a. b. c. d. Identify the congruent triangles in the figure. c. d. 8. M J N K O L a. b. Determine whether given the coordinates of the vertices. Explain. 9. a. Yes; Both triangles have three acute angles. b. No; Each side of triangle PQR is not the same length as the corresponding side of triangle STU. c. No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU. d. Yes; Each side of triangle PQR is the same length as the corresponding side of triangle STU. Refer to the figure. are c. all isosceles triangles. d. X F 14. Triangles ABC and AFD are vertical congruent 72° M equilateral triangles. Find x and y. 38° B C R (2 y+ 6)° A A x+ 4 2x – 3 10. What is ? a. 23 D F b. 38 a. c. 42 b. d. 35 c. 11. What is ? a. 80 d. b. 38 c. 64 15. Triangle RSU is an equilateral triangle. bisects d. 72 . Find x and y. 12. If , what is ? R a. 96 ( y – 2)° b. 124 c. 132 8x + 1 d. 138 13. Triangle FJH is an equilateral triangle. Find x and U S y. T 5x H a. (4 y – 4)° 3x – 8 b. 2x – 1 c. d. J F 16. Triangles ABC and AFD are vertical congruent a. equilateral triangles. Find x and y. b. a. B C b. c. 2x + 9 6y° d. A 5 x – 12 D F Short Answer 17. Write a flow proof for the problem. Prove: X V Given: Prove: A P W Z Y C B R Q Write a two-column proof. 18. Given: R is the midpoint of ; . Prove: S R V U 19. Given: Square GHJK Prove: G H F K J 20. Given: W is the midpoint of and ; . Review 4 Answer Section MULTIPLE CHOICE 1. ANS: D An acute triangle has 3 acute angles. An obtuse triangle has one obtuse angle. A right triangle has one right angle. Feedback A Check for congruent sides and measure angles. B Check for congruent sides and measure angles. C Check for congruent sides and measure angles. D Correct! PTS: 1 DIF: Average REF: Lesson 4-1 OBJ: 4-1.1 Identify and classify triangles by angles. NAT: NCTM GM.1 | NCTM GM.1a STA: OK 1.2 TOP: Identify and classify triangles by angles. KEY: Triangles | Classify Triangles 2. ANS: C Use the Distance Formula to find the lengths of the sides. If or or , then the triangle is isosceles. If , then the triangle is equilateral. If neither of the above, the triangle is scalene. Feedback A Use the distance formula to find the lengths of the sides. B Did you use the distance formula? C Correct! D What are the lengths of the sides? PTS: 1 DIF: Average REF: Lesson 4-1 OBJ: 4-1.2 Identify and classify triangles by sides. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1 TOP: Identify and classify triangles by sides. KEY: Triangles | Classify Triangles 3. ANS: C The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180. Feedback A What do you know about vertical angles? B What do you know about vertical angles? C Correct! D Use the Angle Sum Theorem. PTS: 1 DIF: Basic REF: Lesson 4-2 OBJ: 4-2.1 Apply the Angle Sum Theorem. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1 TOP: Apply the Angle Sum Theorem. KEY: Angle Sum Theorem 4. ANS: B The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180. Feedback A Did you use the Angle Sum Theorem. B Correct! C Use the Angle Sum Theorem. D Use the Angle Sum Theorem. PTS: 1 DIF: Average REF: Lesson 4-2 OBJ: 4-2.1 Apply the Angle Sum Theorem. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1 TOP: Apply the Angle Sum Theorem. KEY: Angle Sum Theorem 5. ANS: C The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Feedback A What is the sum of the measures of the angles in a triangle? B Did you use the Exterior Angle Theorem? C Correct! D Use the Exterior Angle Theorem. PTS: 1 DIF: Average REF: Lesson 4-2 OBJ: 4-2.2 Apply the Exterior Angle Theorem. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 TOP: Apply the Exterior Angle Theorem. KEY: Exterior Angle Theorem 6. ANS: A The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Feedback A Correct! B What is the sum of the measures of the angles in a triangle? C Did you use the Exterior Angle Theorem? D Use the Exterior Angle Theorem. PTS: 1 DIF: Average REF: Lesson 4-2 OBJ: 4-2.2 Apply the Exterior Angle Theorem. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 TOP: Apply the Exterior Angle Theorem. KEY: Exterior Angle Theorem 7. ANS: C The corresponding sides and angles can be determined from any congruence statement by following the order of the vertices. Feedback A The corresponding sides and angles can be determined from any congruence statement by following the order of the vertices. B The corresponding sides and angles can be determined from any congruence statement by following the order of the vertices. C Correct! D Did you follow the order of the vertices? PTS: 1 DIF: Basic REF: Lesson 4-3 OBJ: 4-3.1 Name and label corresponding parts of congruent triangles. NAT: NCTM GM.1 | NCTM GM.1b | NCTM GM.3 STA: OK 1.2 | OK 1.3 | OK 3.1 TOP: Name and label corresponding parts of congruent triangles. KEY: Corresponding Parts | Congruent Triangles 8. ANS: C The vertices naming the triangles correspond to the congruent vertices of the two triangles in the same order. Feedback A The letters naming the triangles correspond to the congruent vertices of the two triangles. B Be careful with the order of the vertices. C Correct! D Are the vertices in the correct order? PTS: 1 DIF: Average REF: Lesson 4-3 OBJ: 4-3.2 Identify congruent transformations. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 TOP: Identify congruent transformations. KEY: Transformations | Congruence Transformations 9. ANS: D If each side of triangle PQR is the same length as the corresponding side of triangle STU, then the triangles are congruent. Feedback A How do you decide if two triangles are congruent? B Check your math. C Use the SSS Postulate. D Correct! PTS: 1 DIF: Average REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles 10. ANS: B Since is isosceles, . Feedback A Remember the definition of isosceles. B Correct! C Is that the base angle of an isosceles triangle? D Remember the definition of isosceles. PTS: 1 DIF: Basic REF: Lesson 4-6 OBJ: 4-6.1 Use the properties of isosceles triangles. NAT: NCTM GM.1 | NCTM GM.1a STA: OK 1.2 | OK 1.3 | OK 3.3 TOP: Use the properties of isosceles triangles. KEY: Isosceles Triangles 11. ANS: D Since is isosceles, . Feedback A Is that the base angle of an isosceles triangle? B Remember the definition of isosceles. C What do you know about base angles of an isosceles triangle? D Correct! PTS: 1 DIF: Basic REF: Lesson 4-6 OBJ: 4-6.1 Use the properties of isosceles triangles. NAT: NCTM GM.1 | NCTM GM.1a STA: OK 1.2 | OK 1.3 | OK 3.3 TOP: Use the properties of isosceles triangles. KEY: Isosceles Triangles 12. ANS: C ; Feedback A What is the sum of the base angles? B What is the sum of the measures of the angles in a triangle? C Correct! D Is that the vertex angle? PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.1 Use the properties of isosceles triangles. NAT: NCTM GM.1 | NCTM GM.1a STA: OK 1.2 | OK 1.3 | OK 3.3 TOP: Use the properties of isosceles triangles. KEY: Isosceles Triangles 13. ANS: B Feedback A Did you set the two sides equal to each other? B Correct! C How many degrees is each angle of an equilateral triangle? D How many degrees is H? PTS: 1 DIF: Basic REF: Lesson 4-6 OBJ: 4-6.2 Use the properties of equilateral triangles. NAT: NCTM GM.2 | NCTM GM.2a TOP: Use the properties of equilateral triangles. KEY: Equilateral Triangles 14. ANS: A Feedback A Correct! B What do you know about the sides of an equilateral triangle? C How many degrees is each angle of an equilateral triangle? D Did you add or subtract when solving for y? PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.2 Use the properties of equilateral triangles. NAT: NCTM GM.2 | NCTM GM.2a TOP: Use the properties of equilateral triangles. KEY: Equilateral Triangles 15. ANS: D Feedback A Can x be negative? B What is the measure of TRS? C Check your math. D Correct! PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.2 Use the properties of equilateral triangles. NAT: NCTM GM.2 | NCTM GM.2a TOP: Use the properties of equilateral triangles. KEY: Equilateral Triangles 16. ANS: B Feedback A What is the measure of each angle in an equilateral triangle? B Correct! C Did you set the given sides equal to each other? D Check your math. PTS: 1 DIF: Average REF: Lesson 4-6 OBJ: 4-6.2 Use the properties of equilateral triangles. NAT: NCTM GM.2 | NCTM GM.2a TOP: Use the properties of equilateral triangles. KEY: Equilateral Triangles SHORT ANSWER 17. ANS: Given: Prove: A P C B R Q Proof: A flow proof organizes a series of statements in logical order, starting with the given statements. Each statement is written in a box with the reason verifying the statement written below the box. Arrows are used to indicate how the statements relate to each other. If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. PTS: 1 DIF: Advanced REF: Lesson 4-1 OBJ: 4-2.3 Solve multi-step problems. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 | OK 2.1b | OK 4.1 TOP: Solve multi-step problems. KEY: Solve multi-step problems. 18. ANS: Sample: Given: R is the midpoint of ; . Prove: Proof: Statements Reasons 1. R is the midpoint of . 1. Given 2. 2. Midpoint Theorem 3. 3. Given 4. 4. Reflexive Property 5. 5. SSS Postulate PTS: 1 DIF: Basic REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles 19. ANS: Sample: Given: Square GHJK Prove: Proof: Statements Reasons 1. GHJK is a square. 1. Given 2. 2. Definition of a square 3. 3. Definition of a square 4. 4. Reflexive Property 5. 5. SSS Postulate PTS: 1 DIF: Basic REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles 20. ANS: Sample: Given: W is the midpoint of and ; . Prove: Proof: Statements Reasons 1. W is the midpoint of . 1. Given 2. 2. Midpoint Theorem 3. W is the midpoint of . 3. Given 4. 4. Midpoint Theoremt 5. 5. Given 6. 6. SSS Postulate PTS: 1 DIF: Average REF: Lesson 4-4 OBJ: 4-4.1 Use the SSS Postulate to test for triangle congruence. NAT: NCTM GM.1 | NCTM GM.1b STA: OK 1.2 | OK 1.3 TOP: Use the SSS Postulate to test for triangle congruence. KEY: SSS Postulate | Congruent Triangles

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posted: | 12/3/2011 |

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