1. 4.7 Use Isosceles and Equilateral Triangles
Hubarth
Geometry

2. The congruent sides of an isosceles triangle are called legs.
The other side is called the base.
The two angles at the base of the triangle are called the base angles. A
vertex angle
base
angles
leg
leg B C
base
Theorem 4.3
Base Angles Theorem

3. Ex 1. Use the Base Angle Theorem52 N L
Solution

4. Theorem 4.4
Converse of the Base Angle Theorem A B C

5. Ex 2. Use the Converse of the Base Angles Theorem
Find the value of x. F 12 D
X+3 E
Solution

6. Corollary to the Base Angles Theorem
Corollaries
Corollary to the Base Angles Theorem B
Corollary to the Converse of Base Angles Theorem A C

7. Ex 3. Find the Side Length of an Equiangular Triangle
Find the length of each side of the equiangular triangle. 3x
2x+10
Solution
Because the triangle is equiangular, it is also equilateral.
So,
3x=2x+10
x=10
3(10)=30
Each side of the triangle is 30

8. Definition of congruent segments
EX 3 Use Isosceles and Equilateral Triangles
Find the values of x and y in the diagram.
STEP 1
STEP 2
Definition of congruent segments
LN = LM
4 = x + 1
Substitute 4 for LN and x + 1 for LM.
3 = x
Subtract 1 from each side.

9. Practice Find the value of y. y=50 y=9 1. 2. 3. y+4=16 -4 -4 y=12
y=12 9 y 50 y
Y+4 B
5. Find the values of x and y in the diagram. 4. 58
y° = 120°
x° = 60°
6x+4 C A