Isosceles Triangles The congruent sides are the LEGS. The third side is the BASE. The two congruent sides form the VERTEX ANGLE. The other two angles are the BASE ANGLES.

Theorems Theorem 4. 3: Isosceles Triangle Theorem – If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Theorems Theorem 4. 4: CONVERSE of Isosceles Triangle Theorem – If two angles of a triangle are congruent, then the sides opposite the angles are congruent.

Theorems Theorem 4. 5: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

Proof of the Isosceles Triangle Theorem Statements Reasons 1. 2. 3. 4. 5.

Corollaries corollary – a statement that follows immediately from a theorem 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.

Applications Find the value of y.

Solve for x and y

Solve for x

Solve for x

Solve for x

Practice Find the value of y. y=50 1. 50 y=9 2. y y 3. 16 9 y+4=16 -4 -4 y=12 Y+4 5. Find the values of x and y in the diagram. B 4. 58 6 x+4 A y° = 120° x° = 60° C