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

GUIDED PRACTICE for Example 2 3. Find ST in the triangle at the right. SOLUTION STU is equilateral, then its is equiangular Thus ST = 5 ( Base angle theorem ) ANSWER

GUIDED PRACTICE for Example 2 4. Is it possible for an equilateral triangle to have an angle measure other than 60° ? Explain. SOLUTION No; it is not possible for an equilateral triangle to have angle measure other then 60°. Because the triangle sum theorem and the fact that the triangle is equilateral guarantees the angle measure 60° because all pairs of angles could be considered base of an isosceles triangle