1. 4.7 Use Isosceles and Equilateral Triangles

2. Isosceles Triangle
A triangle is isosceles iff it has two or more congruent sides (yes an equilateral triangle is also isosceles)
vertex
Leg
Leg
base angle
base angle
Base

3. Isosceles Triangle Theorem (Base Angles Theorem)
If two sides of a triangle are congruent (isosceles triangle), then the angles opposite them are congruent B C A B C A

4. Use the Isosceles Triangle Theorem

5. Converse of the Isosceles Triangle Theorem (Converse of the Base Angles Theorem)
If two angles of a triangle are congruent, then the sides opposite them are congruent B C A B C A

6. Example
Use the diagram. Copy and complete the statement. Tell what theorem you used.
a.If AE DE, then <___ <___
b.If AB EB, then <___ <___
c.If <D <CED, then ___ ___. E A B C D

7. Corollaries Corollarary to the Base Angles Theorem
If a triangle is equilateral, then it is equiangular
Corollarary to the Converse of the Base Angles Theorem
If a triangle is equiangular, then it is equilateral

8. Example
Find the value of x. x 12
72° x

9. Example
Find the unknown measure. x 15
72° x
42°
42°

10. Example
Find the value of x.
(2x + 9)°
12x°
72°
(4x – 7)°

11. Example
Find the value of x.
40°
80°
2x°
(4x – 6)°

12. Example
Find the unknown measure. x
60°
60° 20 ?

13. Example
Find the value of x. 5
3x°
5x + 5 16 5 5 35

14. Example Find the perimeter of the triangle. (7x - 13) in (x + 29) in
(8x - 15) m
(4x + 3) m
(3x + 5) in
(5x + 8) m