4-5 Isosceles & Equilateral Triangles

1. 4-5 Isosceles & Equilateral Triangles Objectives: To use and apply properties of isosceles and equilateral triangles

2. Solve It!

3. Isosceles vs Equilateral • What is an isosceles triangle? • What is an equilateral triangle? • Label the following on the diagram below: • Legs • Base • Base angle • Vertex angle

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

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

6. Theorem 4-5 • If a line bisects the vertex angle of an isosceles triangle, then the line is also perpendicular bisector of the base.

7. Corollary (4-3) • If a triangle is equilateral, then the triangle is equiangular

8. Corollary (4-4) • If a triangle is equiangular, then the triangle is equilateral

9. Example 1 • Given: G, H, and L are congruent • Is GK = HK ? • Is HL = KJ ? G H K L J

10. Example Two • What is the value of x? 7x – 10 3x + 6

11. Example Three • In the diagram, PLN = LNS. What is the measure of S in the figure below? L P 50º S N

12. Homework Section 4-5 • Page 254 #6-22 evens, 28