Geometry Agenda 1 ENTRANCE 2 Go over Practice

Geometry • Agenda 1. ENTRANCE 2. Go over Practice 3. 4 -5 Isosceles and Equilateral Triangles 4. 4 -6 Congruence in Right Triangles 5. Practice 6. EXIT

Practice 4 -4 Handout

Chapter 4 4 -5 Isosceles and Equilateral Triangles 4 -6 Congruence in Right Triangles

Isosceles Triangle ACB

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

Corollary to Theorem 4 -3 • If a triangle is equilateral, then the triangle is equiangular.

Theorem 4 -4 Converse of Isosceles Triangle Theorem • If two angles of a triangle are congruent, then the sides opposite those angles are congruent. • If then

Corollary to Theorem 4 -4 • If a triangle is equiangular, then the triangle is equilateral.

Theorem 4 -5 • The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. • If bisects BAC, then and

Right Triangle

Theorem 4 -6 Hypotenuse-Leg Theorem (HL) • If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Example #1 • Find x and y.

Example #2 • Find x.

Example #3 • Find x and y.

Example #4 • Find x and y.

Example #5 • Given: PQR is isosceles • Prove: QSP QSR

Example #6 • Are these triangles congruent?

Example #7 • Given: XYZ is isosceles • Prove: XMY ZMY

• Practice – WB 4 -5 # 1 -7, 20 – WB 4 -6 # 2, 5, 6, 7 • EXIT