**Geometry Chapter 4.6 Isosceles, Equilateral, and Right Triangles**

I

**) Vocabulary:**

**A) Base angles**- the two angles adjacent to the base of an isosceles triangle.

**B) Vertex angles**- the angle opposite the base of an isosceles triangle.

**II) Theorems**:

**A) Base Angles Theorem**: if two sides of a triangle are congruent, then the angles opposite them are congruent.

**B) Converse of the Base Angles Theorem**: if two angles of a triangle are congruent, the the sides opposite them are congruent.

**C) Hypotenuse - Leg Congruence Theorem (HL = HL)**: if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.

**Example**: Given Δ ABC and ΔDEF are both right triangles, BC = EF and AC = DF,

then ΔABC = ΔDEF.

**III) Corollaries**:

A) If a triangle is equilateral, then it is equiangular.

B) If a triangle is equiangular, then it is equilateral.