ISOSCELES AND EQUILATERAL

TRIANGLESSection 4-5

VOCABULARY The congruent sides of an isosceles triangle

are its legs. The third side is the base. The two congruent legs form the vertex

angle. The other two angles are the base angles.

ISOSCELES TRIANGLE THEOREM If two sides of a triangle are congruent,

then the angles opposite those sides are congruent.

If then CBAB CA

CONVERSE OF THE ISOSCELES TRIANGLE THEOREM If two angles of a triangle are congruent,

then the sides opposite those angles are congruent.

If then CBAB CA

THEOREM 4-5 If a line bisects the vertex angle of an

isosceles triangle, then the line is also the perpendicular bisector of the base.

MORE THEOREMS… Corollary to Theorem 4-3

If a triangle is equilateral, then the triangle is equiangular.

Corollary to Theorem 4-4 If a triangle is equiangular, then the triangle

is equilateral.

EXAMPLE 1 Complete each statement. 1. DBC ? CDB 2. BED ?___ 3. FED __?___ DFE 4. AB _____ _______

EXAMPLE 2 Solve for x and y. A. x = 180-115 x = 65

y = 180-65-65 y = 50 B. x + 5 = 60 x = 55 y – 10 = 60 y = 70

ASSIGNMENT Pg 254 #6-12, 16-19 show work