1. Find measures in a triangle
EXAMPLE 2
Find measures in a triangle
Find the measures of P, Q, and R.
The diagram shows that PQR is equilateral. Therefore, by the Corollary to the Base Angles Theorem, PQR is equiangular. So, m P = m Q = m R.
3(m P)
= 180 o
Triangle Sum Theorem
m P
= 60 o
Divide each side by 3.
The measures of P, Q, and R are all 60° .
ANSWER

2. GUIDED PRACTICE
for Example 2
Find ST in the triangle at the right.
SOLUTION
STU is equilateral, then its is equiangular
Thus ST = 5
( Base angle theorem )
ANSWER

3. EXAMPLE 3
Use isosceles and equilateral triangles
ALGEBRA
Find the values of x and y in the diagram.
SOLUTION
STEP 1
Find the value of y. Because KLN is equiangular, it is also equilateral and KN KL . Therefore, y = 4.
STEP 2
Find the value of x. Because LNM LMN, LN LM and LMN is isosceles. You also know that LN = 4 because KLN is equilateral.

4. Use isosceles and equilateral triangles
EXAMPLE 3
Use isosceles and equilateral triangles
LN = LM
Definition of congruent segments
4 = x + 1
Substitute 4 for LN and x + 1 for LM.
3 = x
Subtract 1 from each side.

5. GUIDED PRACTICE
for Examples 3 and 4
Find the values of x and y in the diagram.
SOLUTION
y° = 120°
x° = 60°

6. Daily Homework Quiz
Find the value of x. 2.
ANSWER 3

7. Daily Homework Quiz
If the measure of vertex angle of an isosceles triangle is 112°, what are the measures of the base angles? 3.
ANSWER
34°, 34°

8. Daily Homework Quiz
Find the perimeter of triangle. 4.
ANSWER
66 cm