1. Isosceles Triangles & Corollaries

2. Get: ♥ a piece of patty paper ♥ a straight edge ♥ your pencil ♥ your compass ♥ a protractor We are going to create an isosceles triangle with 2 congruent sides.

3. ♥Has at least 2 congruent sides. ♥The angles opposite the congruent sides are congruent ♥Converse is also true. The sides opposite the congruent angles are also congruent. ♥This is a COROLLARY. A corollary naturally follows a theorem or postulate. We can prove it if we need to, but it really makes a lot of sense. Isosceles Triangles

4. ♥The bisector of the vertex angle of an isosceles Δ is the perpendicular bisector of the base. Vertex angle In addition, you just learned that the angles opposite congruent sides are congruent… Base

5. Equilateral Triangle ♥An Equilateral triangle is a special case of an Isosceles Triangle. ♥Remember that an Isosceles Triangle has AT LEAST 2 congruent sides. ♥An Equilateral Triangle is also Equiangular. ♥The bisector of any angle is the perpendicular bisector of the opposite side.

6. Let’s Practice Find the measures of: mFC = mFG = mCG = m<C = m<G = m<F = m<A = m<E = y = 4 4 4 60◦ 70◦ 50 ◦

7. Complete each statement. Explain why it is true.

8. Determine the measure of the indicated angle.  ACB  DCE  BCD

9. Find the value of x and y.

10. An exterior angle of an isosceles triangle has a measure 140. Find two possible sets of measures for the angles of the triangle.

11. Your assignment 4.5 Practice Worksheet