Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent then the sides opposite those angles are congruent. Isosceles Triangle Theorem If two sides of a triangle are congruent then the two angles opposite those sides are congruent. Isosceles Triangle Theorem Converse of the Isosceles Triangle Theorem If two angles of a triangle are congruent then the sides opposite those angles are congruent. Isosceles Triangle Theorem If two sides of a triangle are congruent then the two angles opposite those sides are congruent. Isosceles Triangle Theorem Definition of Altitude Definition of Altitude a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). There are four parts of an isosceles triangle There are four parts of an isosceles triangle 1) 1) 2) 2) 3) 3) 4) 4) Definition of Isosceles Triangle Definition of Isosceles Triangle A triangle with two congruent sides and two congruent angles. A triangle with two congruent sides and two congruent angles. Perpendicular Bisector Theorem: Perpendicular Bisector Theorem: If a line or line segment bisects the vertex angle of an isosceles triangle, then it is also the perpendicular bisector of the opposite side. If a line or line segment bisects the vertex angle of an isosceles triangle, then it is also the perpendicular bisector of the opposite side. Altitude / Perpendicular Bisector Altitude / Perpendicular Bisector 1) What is the sum of all the angles in a triangle? 2) How many angles are in a triangle? 1) What is the sum of all the angles in a triangle? 2) How many angles are in a triangle? Each angle in an equilateral triangle measures ______ Each angle in an equilateral triangle measures ______ Equilateral Triangle Equilateral Triangle A triangle that has all congruent sides (equilateral) and all congruent angles (equiangular). Examples A triangle that has all congruent sides (equilateral) and all congruent angles (equiangular). Examples Scalene Triangle Scalene Triangle
