4 4 Using Triangle Congruence Objectives Use congruence

4. 4 Using Triangle Congruence Objectives: - Use congruence of triangles to conclude congruence of corresponding parts. - Develop and use the Isosceles Triangle Theorem Warm-Up: Statements A B D C Reasons

An isosceles triangle is a triangle with at least two congruent sides. The two congruent sides are known as the legs of the triangle, and the remaining side is known as the base. The angles whose vertices are the endpoints of the base are known as base angles, and the angle opposite the base is known as the vertex angle. VERTEX ANGLE LEGS BASE ANGLES BASE

Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of the Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Corollary: A corollary of a theorem is an additional theorem that can easily be derived from the original theorem. Once theorem is known, the corollary should seem obvious. A corollary can be used as a reason in a proof, just like a theorem or postulate.

Corollary: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Examples: What is the length of BA? B A X Y Z What is the measure of <Y? C

Examples: Find each indicated measure. X <X=___ K KL=___ <Z=___ Y M L Z E Q F <F=___ QR=___ P R G

Examples: Find each indicated measure. B H <ABD=___ GH=___ J A D C G Y X <X=___ Z F

Examples: Find each indicated measure. <T=___ U 8 x T 6 x V

Examples: Find each indicated measure. D F <F=___ <E=___ E If EF = 3 x-12 then ED = ___

Examples: Find each indicated measure. X W XZ=___ Y Z

Examples: Find each indicated measure. L <N=___ N M

Examples: Find each indicated measure. x=___ AC=___ y=___ B BC=___ <A=___ 8 3 x-y A x+3 y+2 C

Homework: Practice Worksheet

Recall that the Polygon Congruence Postulate states that if two triangles are congruent then their corresponding parts are congruent. E B D A C F This idea is often stated in the following form: Corresponding Parts of Congruent Triangles are Congruent, abbreviated as CPCTC.

Given: ------Prove: ----- STATEMENTS REASONS