Find measures in a triangle

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Presentation transcript:

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

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

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.

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.

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

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

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°

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