1. Objectives: Use properties of isosceles and equilateral triangles
Use properties of right triangles

2. Properties of Isosceles Triangles
In lesson 4.1, you learned that a triangle is an isosceles if it has at least two congruent sides.
The two angles adjacent to the base are the base angles. The angle opposite the base is the vertex angle.

3. Remember:
An EQUILATERAL triangle is a special type of isosceles triangle.

4. Equilateral and Isosceles Triangles
Find the value of x
Find the value of y
3x = 180
X = 60 y° x°

5. Ex. 2: Using Equilateral and Isosceles Triangles
Find the value of x
Find the value of y
120° + 2y° = 180°
2y = 60
y = 30 y° x°
60°

6. Using Properties of Right Triangles
You have learned four ways to prove that triangles are congruent.
Side-Side-Side (SSS)
Side-Angle-Side (SAS)
Angle-Side-Angle (ASA)
Angle-Angle-Side (AAS)

7. Solve:
Solution: Isosceles Triangle X = X=72

8. Solve: Solution: Two Isosceles Triangles 90- 28 = 62 180-62-62 = 56
= 62
= 56
X=56

9. Solve: Solution: Two Isosceles Triangles 180 – 65-65 = 50
180 – = 80
X= 80 50 50
=80 50

10. Solve: Solution: 120 = 60+60 60= 60 vertical angles X = 60 60 60 60 60

11. Try this one:
Solution: 12 = 2x = 2x X = 12

12. One More: Solution: 180-68-68 = 44 90 - 44 = 46 4x – 2 = 46
Solve for x
4x = 48
X = 12 44 68

13. Last One:
Solution:
146 = 13x + 3
143 = 13x 11