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Name: ________________________ Class: ___________________ Date: __________ ID: A AAS, ASA, and HL Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. 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. 2. Determine if you can use ASA to prove ∆CBA ≅ ∆CED. Explain. a. b. c. d. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. No other congruence relationships can be determined, so ASA cannot be applied. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Adjacent Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by SAS. 1 Name: ________________________ ____ ID: A 3. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. a. b. c. d. ∆ABC ≅ ∆ABC ≅ ∆ABC ≅ ∆ABC ≅ ∆JLK , HL ∆JKL, HL ∆JLK , SAS ∆JKL, SAS 2 ID: A AAS, ASA, and HL Quiz Answer Section MULTIPLE CHOICE 1. ANS: C Statements 2 and 3 determine the measures of two angles of the triangle. Statement 1 determines the length of the included side. By ASA, the triangle must be unique. Feedback A B C D Draw a diagram. There is enough information to determine a unique triangle. There is not enough information for SAS. Draw a diagram to help you. Correct! There is not enough information for SSS. Draw a diagram to help you. PTS: 1 DIF: Average REF: 1a814442-4683-11df-9c7d-001185f0d2ea OBJ: 4-5.1 Problem-Solving Application LOC: MTH.C.14.06.01.005 TOP: 4-5 Triangle Congruence: ASA, AAS, and HL KEY: application | triangle congruence DOK: DOK 2 2. ANS: C AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. Feedback A B C D Look for vertical angles. Adjacent angles are angles in a plane that have their vertex and one side in common but have no interior points in common. Angle ACB and angle DCE are not adjacent angles. Correct! Use ASA, not SAS, to prove the triangles congruent. PTS: OBJ: LOC: KEY: 1 DIF: Basic 4-5.2 Applying ASA Congruence MTH.C.11.08.02.02.02.006 proof | congruent triangles | ASA REF: STA: TOP: DOK: 1 1a816b52-4683-11df-9c7d-001185f0d2ea NY.NYLES.MTH.05.GEO.G.G.28 4-5 Triangle Congruence: ASA, AAS, and HL DOK 2 ID: A 3. ANS: B Because ∠BAC and ∠KJL are right angles, ∆ABC and ∆JKL are right triangles. You are given a pair of congruent legs AC ≅ JL and a pair of congruent hypotenuses CB ≅ LK . So a hypotenuse and a leg of ∆ABC are congruent to the corresponding hypotenuse and leg of ∆JKL. ∆ABC ≅ ∆JKL by HL. Feedback A B C D Segment AC is congruent to segment JL. Make sure the triangle vertices correspond accordingly. Correct! Segment AC is congruent to segment JL. Make sure the triangle vertices correspond accordingly. For SAS, the angle is included between the sides. For SAS, the angle is included between the sides. PTS: STA: LOC: TOP: DOK: 1 DIF: Advanced REF: 1a86300a-4683-11df-9c7d-001185f0d2ea NY.NYLES.MTH.05.GEO.G.G.28 MTH.C.11.08.02.02.02.010 | MTH.C.11.08.02.02.02.011 4-5 Triangle Congruence: ASA, AAS, and HL KEY: proof | congruent triangles | HL DOK 3 2 Name: ________________________ Class: ___________________ Date: __________ AAS, ASA, and HL Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Determine if you can use ASA to prove ∆CBA ≅ ∆CED. Explain. a. b. c. d. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by SAS. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. No other congruence relationships can be determined, so ASA cannot be applied. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Adjacent Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. 1 ID: B Name: ________________________ ____ 2. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. a. b. c. d. ____ ID: B ∆ABC ≅ ∆ABC ≅ ∆ABC ≅ ∆ABC ≅ ∆JLK , SAS ∆JKL, HL ∆JLK , HL ∆JKL, SAS 3. 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. Yes. They form a unique triangle by SAS. Yes. They form a unique triangle by SSS. Yes. They form a unique triangle by ASA. No. There is no unique configuration. 2 ID: B AAS, ASA, and HL Quiz Answer Section MULTIPLE CHOICE 1. ANS: A AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. Feedback A B C D Correct! Use ASA, not SAS, to prove the triangles congruent. Look for vertical angles. Adjacent angles are angles in a plane that have their vertex and one side in common but have no interior points in common. Angle ACB and angle DCE are not adjacent angles. PTS: 1 DIF: Basic REF: 1a816b52-4683-11df-9c7d-001185f0d2ea OBJ: 4-5.2 Applying ASA Congruence STA: NY.NYLES.MTH.05.GEO.G.G.28 LOC: MTH.C.11.08.02.02.02.006 TOP: 4-5 Triangle Congruence: ASA, AAS, and HL KEY: proof | congruent triangles | ASA DOK: DOK 2 2. ANS: B Because ∠BAC and ∠KJL are right angles, ∆ABC and ∆JKL are right triangles. You are given a pair of congruent legs AC ≅ JL and a pair of congruent hypotenuses CB ≅ LK . So a hypotenuse and a leg of ∆ABC are congruent to the corresponding hypotenuse and leg of ∆JKL. ∆ABC ≅ ∆JKL by HL. Feedback A B C D Segment AC is congruent to segment JL. Make sure the triangle vertices correspond accordingly. For SAS, the angle is included between the sides. Correct! Segment AC is congruent to segment JL. Make sure the triangle vertices correspond accordingly. For SAS, the angle is included between the sides. PTS: STA: LOC: TOP: DOK: 1 DIF: Advanced REF: 1a86300a-4683-11df-9c7d-001185f0d2ea NY.NYLES.MTH.05.GEO.G.G.28 MTH.C.11.08.02.02.02.010 | MTH.C.11.08.02.02.02.011 4-5 Triangle Congruence: ASA, AAS, and HL KEY: proof | congruent triangles | HL DOK 3 1 ID: B 3. ANS: C Statements 2 and 3 determine the measures of two angles of the triangle. Statement 1 determines the length of the included side. By ASA, the triangle must be unique. Feedback A B C D There is not enough information for SAS. Draw a diagram to help you. There is not enough information for SSS. Draw a diagram to help you. Correct! Draw a diagram. There is enough information to determine a unique triangle. PTS: OBJ: TOP: DOK: 1 DIF: Average REF: 1a814442-4683-11df-9c7d-001185f0d2ea 4-5.1 Problem-Solving Application LOC: MTH.C.14.06.01.005 4-5 Triangle Congruence: ASA, AAS, and HL KEY: application | triangle congruence DOK 2 2 Name: ________________________ Class: ___________________ Date: __________ AAS, ASA, and HL Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Determine if you can use ASA to prove ∆CBA ≅ ∆CED. Explain. a. b. c. d. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. No other congruence relationships can be determined, so ASA cannot be applied. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by SAS. AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Adjacent Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. 1 ID: C Name: ________________________ ____ 2. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it. a. b. c. d. ____ ID: C ∆ABC ≅ ∆ABC ≅ ∆ABC ≅ ∆ABC ≅ ∆JKL, SAS ∆JLK , SAS ∆JKL, HL ∆JLK , HL 3. 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. Yes. They form a unique triangle by SSS. Yes. They form a unique triangle by SAS. No. There is no unique configuration. Yes. They form a unique triangle by ASA. 2 ID: C AAS, ASA, and HL Quiz Answer Section MULTIPLE CHOICE 1. ANS: B AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA. Feedback A B C D Look for vertical angles. Correct! Use ASA, not SAS, to prove the triangles congruent. Adjacent angles are angles in a plane that have their vertex and one side in common but have no interior points in common. Angle ACB and angle DCE are not adjacent angles. PTS: 1 DIF: Basic REF: 1a816b52-4683-11df-9c7d-001185f0d2ea OBJ: 4-5.2 Applying ASA Congruence STA: NY.NYLES.MTH.05.GEO.G.G.28 LOC: MTH.C.11.08.02.02.02.006 TOP: 4-5 Triangle Congruence: ASA, AAS, and HL KEY: proof | congruent triangles | ASA DOK: DOK 2 2. ANS: C Because ∠BAC and ∠KJL are right angles, ∆ABC and ∆JKL are right triangles. You are given a pair of congruent legs AC ≅ JL and a pair of congruent hypotenuses CB ≅ LK . So a hypotenuse and a leg of ∆ABC are congruent to the corresponding hypotenuse and leg of ∆JKL. ∆ABC ≅ ∆JKL by HL. Feedback A B C D For SAS, the angle is included between the sides. Segment AC is congruent to segment JL. Make sure the triangle vertices correspond accordingly. For SAS, the angle is included between the sides. Correct! Segment AC is congruent to segment JL. Make sure the triangle vertices correspond accordingly. PTS: STA: LOC: TOP: DOK: 1 DIF: Advanced REF: 1a86300a-4683-11df-9c7d-001185f0d2ea NY.NYLES.MTH.05.GEO.G.G.28 MTH.C.11.08.02.02.02.010 | MTH.C.11.08.02.02.02.011 4-5 Triangle Congruence: ASA, AAS, and HL KEY: proof | congruent triangles | HL DOK 3 1 ID: C 3. ANS: D Statements 2 and 3 determine the measures of two angles of the triangle. Statement 1 determines the length of the included side. By ASA, the triangle must be unique. Feedback A B C D There is not enough information for SSS. Draw a diagram to help you. There is not enough information for SAS. Draw a diagram to help you. Draw a diagram. There is enough information to determine a unique triangle. Correct! PTS: OBJ: TOP: DOK: 1 DIF: Average REF: 1a814442-4683-11df-9c7d-001185f0d2ea 4-5.1 Problem-Solving Application LOC: MTH.C.14.06.01.005 4-5 Triangle Congruence: ASA, AAS, and HL KEY: application | triangle congruence DOK 2 2