1. Lesson 9
Lines & Angles
Special Triangles

2. Warm-Up Two angles in a triangle are listed. Find the measure of
the third angle.
90º, 30º, ____
129º, 42º, ____
22º, 55º, ____
22.5º, 46.3º, ____

3. Special Triangles Target:
Find measures of angles in isosceles and equilateral triangles.

4. Vocabulary
Equiangular: All angles have the same measure.

7. Equilateral and Isosceles Triangle Angle Properties
Equilateral Triangle: Each angle in an equilateral triangle is 60°.
Isosceles Triangle : The angles which are across from
the congruent sides will be equal in measure.

8. Example 1
ΔMNP is an equilateral triangle. The measure of M is (2x + 6)°. Find the value of x. Each angle in an equilateral triangle is 60°. Set the angle equal to 60°. 2x + 6 = 60 Subtract 6 from each side. –6 –6 2x = 54 Divide by 2 on each side. 2 2 x = 27 The value of x is 27.

9. Example 2 Find the value of x.
The triangle is isosceles. The angles that are across from the congruence marks must be equal. So,
112 + x + x = 180
Combine like terms x = 180
Subtract 112 from each side. – –112
2x = 68
Divide by 2 on each side
x = 34
The value of x is 34.

10. Exit Problems
Find the value of x.

11. Communication Prompt
Do you think there are any special angle relationships in
a scalene triangle? Explain your answer.