Isosceles, Equilateral, and Right Triangles Sec 4.6 GOAL: To use properties of isosceles, equilateral and right triangles To use RHL Congruence Theorem

Definitions Isosceles Triangle – a triangle that has at least two congruent sides called legs. If a triangle has three congruent sides, it is called an Equilateral Triangle. Leg Base (noncongruent side) Base Angles Vertex Angle Each angle measures 60 degrees

Base Angles Theorem Base Angles Theorem – If two sides of a triangle are congruent, then the angles opposite them are congruent. A B C

Converse of the Base Angles Theorem Converse of the Base Angles Theorem – If two angles of a triangle are congruent, then the sides opposite them are congruent. A B C

Corollaries If a triangle is equilateral, then it is equiangular. If a triangle is equiangular, then it is equilateral. Is an equilateral triangle an isosceles triangle? Is an isosceles triangle an equilateral triangle?

Example Find x and y.

Hypotenuse – Leg (HL) Congruence Hypotenuse – Leg (HL) Congruence – If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. A CB D F E

Two – Column Proof Given: Prove: A CB D F E

Examples Find x or y

Examples Are you given enough information to prove the triangles congruent?