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Warm-up SSS AAS Not possible HL Not possible SAS 4.6 Isosceles, Equilateral, and Right Triangles Students will use the Isosceles Base Angles Theorem and the HL theorem to prove triangles congruent. A Given: ABC, AB AC, D is the midpoint of CB. Prove: B C C D B Base Angles Theorem • If two sides of a triangle are congruent, then the angles opposite them are congruent. • If AB ,AC then A B C. B C Converse of the Base Angles Theorem • If two angles of a triangle are congruent, then the sides opposite them are congruent. • If B C, then AB .AC Corollary to the Base Angles Theorem • If a triangle is equilateral, then it is equiangular. Corollary to the Converse of the Base Angles Theorem • If a triangle is equiangular, then it is equilateral. Hypotenuse-Leg (HL) Congruence Theorem • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. • If , then ABC DEF. BC EF and AC DF A B D C E F Example Proof: • The television antenna is to the plane containing the points B, C, D, and E. Each of the stays running from the top of the antenna to B, C, and D uses the same length of cable. Prove that AEB, AEC, and AED are congruent. • Given: AEEB, AEEC, AEED, AB AC AD • Prove: AEB AEC AED Cool Down