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GOAL

4.1. Triangles and Angles. CLASSIFYING TRIANGLES. 1. GOAL. EXAMPLE 1. Learn the vocabulary!!!. A. 60 °. 60 °. 60 °. B. C. Extra Example 1. Classify the triangle. Since the 3 angles are congruent, it is equiangular , and since the 3 sides are congruent, it is also equilateral. G.

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GOAL

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

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

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

  4. 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. Extra Example 2

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

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

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

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

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

  10. A x° B C 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.

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

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