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# 4.1 triangles and angles

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### 4.1 triangles and angles

1. 1. Triangles and Angles
2. 2. Triangles Triangle – 3 segments joining 3 non-collinear points, called vertices.
3. 3. Classification By Sides Classification By Angles
4. 4. Classifying Triangles • In classifying triangles, be as specific as possible. Acute, Scalene Obtuse, Isosceles
5. 5. Theorem 4.1 – Triangle Sum Theorem • The sum of the measures of the interior angles of a triangle is 180o . m A + m∠ B + m C = 180∠ ∠ o
6. 6. To Prove Given: ΔABC Prove: m 1 + m 2 + m 3 = 180∠ ∠ ∠ o Parallel Postulate 2. m 4 + m∠ 2 + m 5 = 180∠ ∠ o Angle addition postulate, def’n of a straight angle 3. 1 4, 3 5∠ ≅ ∠ ∠ ≅ ∠ Alternate interior angles theorem 4. m 1 = m 4, m 3 = m 5∠ ∠ ∠ ∠ Definition of congruent angles 5. m 1 + m 2 + m 3 = 180∠ ∠ ∠ o Substitution property of equality
7. 7. Corollary to Triangle Sum Theorem • A corollary is a statement that readily follows from a theorem. The acute angles of a right triangle are complementary. m A + m∠ B = 90∠ o
8. 8. Example 1 Find the value of x in the diagram.
9. 9. Theorem 4.2- Exterior Angles Theorem • The measure of an exterior angle is equal to the sum of the measures of the 2 non-adjacent interior angles. m 1 = m∠ A + m B∠ ∠
10. 10. Example 2 Solve for y in the diagram.
11. 11. Checkpoint: Complete the exercises.
12. 12. Homework • Exercise 4.1 page 198: 1-47, odd.