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
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
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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.1 Naming Congruent Corresponding Parts NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.C.11.01.02.03.002 MTH.C.11.02.02.002 TOP: 4-3 Congruent Triangles KEY: correspondence corresponding parts DOK: DOK 1 1
ID: A 2. ANS: B m DCE + m CED + m EDC = 180 Triangle Sum Theorem m DCE + 23 + 90 = 180 Substitution. m DCE + 113 = 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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.2 Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.G.30 NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C.11.02.02.001 MTH.C.11.03.02.04.002 TOP: 4-3 Congruent Triangles KEY: triangle sum theorem congruent triangles corresponding parts DOK: DOK 2 2
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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.3 Proving Triangles Congruent NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.PS.4 NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.P.08.02.03.017 MTH.C.11.08.02.02.002 TOP: 4-3 Congruent Triangles KEY: proof congruent triangles DOK: DOK 1 3
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
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
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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.1 Naming Congruent Corresponding Parts NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.C.11.01.02.03.002 MTH.C.11.02.02.002 TOP: 4-3 Congruent Triangles KEY: correspondence corresponding parts DOK: DOK 1 1
ID: B 2. ANS: A m DCE + m CED + m EDC = 180 Triangle Sum Theorem m DCE + 23 + 90 = 180 Substitution. m DCE + 113 = 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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.2 Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.G.30 NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C.11.02.02.001 MTH.C.11.03.02.04.002 TOP: 4-3 Congruent Triangles KEY: triangle sum theorem congruent triangles corresponding parts DOK: DOK 2 2
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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.3 Proving Triangles Congruent NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.PS.4 NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.P.08.02.03.017 MTH.C.11.08.02.02.002 TOP: 4-3 Congruent Triangles KEY: proof congruent triangles DOK: DOK 1 3
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
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
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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.1 Naming Congruent Corresponding Parts NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.C.11.01.02.03.002 MTH.C.11.02.02.002 TOP: 4-3 Congruent Triangles KEY: correspondence corresponding parts DOK: DOK 1 1
ID: C 2. ANS: B m DCE + m CED + m EDC = 180 Triangle Sum Theorem m DCE + 23 + 90 = 180 Substitution. m DCE + 113 = 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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.2 Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.G.30 NY.NYLES.MTH.05.GEO.G.G.36 LOC: MTH.C.11.02.02.001 MTH.C.11.03.02.04.002 TOP: 4-3 Congruent Triangles KEY: triangle sum theorem congruent triangles corresponding parts DOK: DOK 2 2
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-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.3 Proving Triangles Congruent NAT: NT.CCSS.MTH.10.9-12.G.SRT.5 STA: NY.NYLES.MTH.05.GEO.G.PS.4 NY.NYLES.MTH.05.GEO.G.RP.2 LOC: MTH.P.08.02.03.017 MTH.C.11.08.02.02.002 TOP: 4-3 Congruent Triangles KEY: proof congruent triangles DOK: DOK 1 3