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Warmup Are the triangles congruent? Explain why or why not. Write the congruence statements for each pair of sides or angles in your explanation. A Given: C is the midpoint of both 𝑨𝑬 and 𝑩𝑫. C D B E Are the triangles congruent? Explain why or why not. Write the congruence statements for each pair of sides or angles in your explanation. Given: C is the midpoint of both 𝑨𝑬 and 𝑩𝑫. A C D B E • 𝑨𝑪 ≅ 𝑬𝑪 because C is the midpoint of 𝑨𝑬. • 𝑩𝑪 ≅ 𝑫𝑪 because C is the midpoint of 𝑩𝑫. • ∠𝑨𝑪𝑩 ≅ ∠𝑬𝑪𝑫 because vertical angles are congruent. • So the triangles are congruent by SAS. Let’s Review! ◦We can prove triangles are congruent by ◦ Rigid Motions ◦ Knowing all sides AND angles are congruent ◦What we learned yesterday was that we do not need to know that all sides are congruent and all angles are congruent to prove two triangles are congruent. Let’s Review ◦There are shortcuts we can use to prove triangles are congruent! ◦We can prove triangles are congruent if ◦ We know all sides are congruent (SSS) ◦ We know two sides are congruent and the included angle is congruent (SAS) A Video… https://www.khanacademy.org/math/geometry/congruence/trianglecongruence/v/more-on-why-ssa-is-not-a-postulate SSA is not a shortcut! Write down when it is not a shortcut. Remember: For right triangles… HL Congruence (Special Case of SSA) Example of HL Congruence Which rigid motion??? Objective: Explore Triangle Congruence Triangle Angle Sum Theorem All of the angles in a triangle sum to 180 degrees Discuss with your trio Do you think that AAA works as a shortcut? ◦In other words, if we know all of the angles of two triangles are congruent, do we know that the two triangles are congruent? AAA is not a shortcut! Write down why it is not a shortcut. An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side. ASA Activity Construct a triangle with a 3 inch straw and angles given to you. The three inch straw will be your included side. You will have to cut up the straw to construct the other two side lengths. Compare your triangle with the triangles made by other in your group. Is it possible to construct different triangles from the same three parts? Are your triangles congruent? ASA Congruence Example of ASA Congruence Determine if you can use ASA to prove NKL LMN. Explain. By the Alternate Interior Angles Theorem. KLN MNL and KNL MLN. NL LN by the Reflexive Property. So ASA can be applied. SAA Activity Construct a triangle from the two angles given and a 3 inch straw. The 3 inch straw should be the unincluded side. You will have to cut up a straw to come up with your other two side lengths. Compare your triangle with the other triangles at your table. Is it possible to construct different triangles from the same three parts, or will all the triangles be congruent? AAS Congruence Example of AAS Congruence Given: 𝑱𝑳 𝒃𝒊𝒔𝒆𝒄𝒕𝒔 ∠𝑲𝑳𝑴 Determine if you can use AAS to prove that the triangles are congruent. Write Down all the Three Letter Variations of the Combinations of the letters A and S For example: SSS Circle which ones work as shortcuts and which ones do not work as shortcuts Group the ones that mean the same thing! For example: AAS is the same as SAA Works As a Shortcut Does Not Work As a Shortcut SSS SAS HL ASA AAS/SAA SSA * AAA *works in some cases Homework ASA pg. 1007-1008 (3-6) AAS pg. 1060 (1-7)