Section 4 4 The Isosceles Triangle Theorems vertex

Section 4 -4: The Isosceles Triangle Theorems

vertex leg angle leg base angle

Isosceles Triangle Definition: A triangle with at least two congruent sides ____________________

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

Corollary 1: An equilateral triangle is also equiangular ___________. Corollary 2: An equilateral triangle has three 60° _____ angles.

Corollary 3: The bisector of the vertex angle of an perpendicular isosceles triangle is __________ to the midpoint base at its ______. Corollary 4: An equiangular triangle is also equilateral ____________.

x = 70 y = 40 x = 75 y = 75

2 x – 4 = x + 5 x=9 2 x + 7 = 5 x – 8 15 = 3 x x=5

62° (2 x)° x = 42 2 x + x = 180 5 x = 180 x = 36

40° 65° x = 50 70° x = 50

d; Given b; a; Substitution Prop c; Converse of Isosceles Triangle

• Given Substitution Prop.

HOMEWORK: page 137 #1 -10 all (#9, 10 give reasons)