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Name: ______________________________________________________ Date: __________________ Per: _______ LC Math 2 Adv β Additional Triangle Congruence Criteria (LT 8) Exploratory Challenge Today we are going to examine four possible triangle congruence criteria, Angle-Angle-Side (AAS), Side-Side-Angle (SSA), AngleAngle-Angle (AAA), and Hypotenuse-Leg (HL). Ultimately, only some of these criteria ensure congruence. ANGLE-ANGLE-SIDE TRIANGLE CONGRUENCE CRITERIA (AAS): Given two triangles β³ π΄π΅πΆ and β³ π΄β²π΅β²πΆβ². If π΄π΅ = π΄β²π΅β² (Side), πβ π΅ = πβ π΅β² (Angle), and πβ πΆ = πβ πΆβ² (Angle), then the triangles are congruent. Consider a pair of triangles that meet the AAS criteria. If you knew that two angles of one triangle corresponded to and were equal in measure to two angles of the other triangle, what conclusions can you draw about the third angle of each triangle? Given this conclusion, which formerly learned triangle congruence criteria can we use to determine if the pair of triangles are congruent? Therefore, the AAS criterion is actually an extension of the triangle congruence criterion. HYPOTENUSE-LEG TRIANGLE CONGRUENCE CRITERIA (HL): Given two right triangles β³ π΄π΅πΆ and β³ π΄β²π΅β²πΆβ²with right angles π΅ and π΅β². If π΄π΅ = π΄β²π΅β² (Leg) and π΄πΆ = π΄β²πΆβ² (Hypotenuse), then the triangles are congruent. As with some of our other proofs, we do not start at the very beginning, but imagine that a congruence exists so that triangles have been brought together such that π΄ = π΄β² and πΆ = πΆβ²; the hypotenuse acts as a common side to the transformed triangles. If you knew that two sides of one right triangle corresponded to and were equal in measure to two angles of the other right triangle, what conclusions can you draw about the third side of each triangle? Given this conclusion, which formerly learned triangle congruence criteria can we use to determine if the pair of triangles are congruent? Therefore, the AAS criterion is actually an extension of the _____ triangle congruence criterion. SIDE-SIDE-ANGLE (SSA): Given two triangles β³ π΄π΅πΆ and β³ π΄β²π΅β²πΆβ². If πβ π΄ = πβ π΄β² (Angle), π΄π΅ = π΄β²π΅β² (Side), π΅πΆ = π΅β²πΆβ² (Side), then the triangles are congruent. Visit the website: goo.gl/thd9kp Construct a triangle using the sides mentioned in the congruence criteria above. Then determine if all triangles constructed with the congruent corresponding parts will be congruent. Summarize your findings below: Therefore, the SSA criteria isβ¦ ANGLE-ANGLE-ANGLE (AAA): Given two triangles β³ π΄π΅πΆ and β³ π΄β²π΅β²πΆβ². If πβ π΄ = πβ π΄β² (Angle), πβ π΅ = πβ π΅β² (Angle), πβ πΆ = πβ πΆβ² (Angle), then the triangles are congruent. Visit the website: goo.gl/thd9kp Construct a triangle using the sides mentioned in the congruence criteria above. Then determine if all triangles constructed with the congruent corresponding parts will be congruent. Summarize your findings below: Therefore, the AAA criteria isβ¦ List all the triangle congruence criteria here: List the criteria that do not determine congruence here: