1. GOAL 1 CLASSIFYING TRIANGLES EXAMPLE 1 4.1 Triangles and Angles Learn the vocabulary!!!

2. Extra Example 1 Classify the triangle. 60° A BC Since the 3 angles are congruent, it is equiangular, and since the 3 sides are congruent, it is also equilateral.

3. Checkpoint EXAMPLE 2 Classify the triangle. G H I 88° 46° acute isosceles

4. Extra Example 2 a. The diagram shows a bridge. Explain why is an isosceles right triangle. Since MN = NO and is a right angle, is an isosceles right triangle by definition.

5. Extra Example 2 (cont.) b. Identify the legs and hypotenuse of Which side is the base of the triangle?

6. Checkpoint 6 8 10 J K L a. Explain why the triangle is a scalene right triangle. b. Explain why there is no base in the triangle. It has one right angle and no side lengths are the same. The triangle is not isosceles.

7. GOAL 2 USING ANGLE MEASURES OF TRIANGLES EXAMPLE 3 4.1 Triangles and Angles TRIANGLE SUM THEOREMEXTERIOR ANGLE THEOREM Study these theorems as you go on!

8. Extra Example 3 Find the value of x. Then find the measure of the exterior angle. 72° x°x° (2x – 11)° To find x, apply the Exterior Angle Theorem: x° + 72° = (2x – 11)° 83 = x Then substitute to find the measure of the exterior angle: (283 – 11)° = 155°.

9. Checkpoint Find the value of x. Then find the measure of the exterior angle. 110° x°x° (4x – 7)° x = 39 The measure of the exterior angle is 149°. EXAMPLE 4 Be sure to study the before going on! COROLLARY TO THE TRIANGLE SUM THEOREM

10. Extra Example 4 The measure of one acute angle of a right triangle is one- fourth the measure of the other acute angle. Find the measure of each acute angle. x°x° A BC

11. Checkpoint The measure of one acute angle of a right triangle is five times the measure of the other acute angle. Find the measure of each acute angle. 15°, 75°

12. QUESTION: ANSWER: What are some ways to classify a triangle by sides? by angles? sides: equilateral, isosceles, scalene angles: acute, obtuse, right, equiangular