Warm-up AAS SSS Not possible HL Not possible SAS.

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Presentation transcript:

Warm-up AAS SSS 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.

Given: Prove:  B   C A B C D

Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. If, then  B   C. A BC

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.

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 and, then  ABC   DEF. A BC D 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: Prove:  AEB   AEC   AED

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