Lesson 9 Lines & Angles Special Triangles.

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Presentation transcript:

Lesson 9 Lines & Angles Special Triangles

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, ____

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

Vocabulary Equiangular: All angles have the same measure.

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.

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.

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. 112 + 2x = 180 Subtract 112 from each side. –112 –112 2x = 68 Divide by 2 on each side. 2 2 x = 34 The value of x is 34.

Exit Problems Find the value of x.

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