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

2. 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

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

4. 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

5. 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?

6. Example Find x and y.

7. 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

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

9. Examples Find x or y

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