1. Lesson 1.5
Core Focus on Geometry
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, ____
60 9
103
111.2

3. Find measures of angles in isosceles and equilateral triangles.
Lesson 1.5
Special Triangles
Find measures of angles in isosceles and equilateral triangles.

4. Explore! What Makes Me Special?
Step 1 Two equilateral triangles are drawn below. Measure the angles inside each triangle and list them on your own paper.
Step 2 Based on Lesson 1.4, what should the sum of the angle measures of each triangle equal?
Step 3 Is the sum of m∠A, m∠B and m∠C equal to 180°? If not, check your measurements. Is the sum of m∠D, m∠E and m∠F equal to 180°? If not,
check your measurements.
Step 4 Do you notice anything about the measure of each angle in an equilateral triangle? If so, what is your discovery?

5. Explore! What Makes Me Special?
Step 5 Use division to show how you could calculate the degree measure of an angle in an equilateral triangle.
Step 6 Use a ruler to draw two isosceles triangles. Remember that two sides must be the same length in an isosceles triangle.
Step 7 Measure the angles in your triangles. There should be two angles in each triangle that are equal to each other. Where are those angles in comparison to the two sides that are equal?

6. 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 equal to 60. Set the angle equal to 60. Subtract 6 from each side of the equation. Divide both sides of the equation by 2. The value of x is 27.
2x + 6 = 60
– 6 – 6
2x = 54 a
x = 27

9. Example 2 x + x + 112 = 180 2x + 112 = 180 –112 –112 2x = 68a 2 2aa
Find the value of x. The triangle is isosceles. The angles that are across from the congruence marks must be equal so: The sum of the angles is 180. Combine like terms. Subtract 112 from both sides of the equation. Divide both sides of the equation by 2. The value of x is 34.
x + x = 180
2x = 180
–112 –112
2x = 68a aa
x = 34a

10. Communication Prompt
Explain why it makes sense that the angles in a scalene triangle will all be different measures.

11. Exit Problems Find the value of x. 1. 2. 3. x = 12 x = 5 x = 37 4x 5
48
4x 5
12x
32
2x
x = 12
x = 5
x = 37