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1. 90º

~. 4. How do you know that 1 = 2?. 2. 1. Classify each angle as acute, obtuse, or right. 1. 90º. 2. 72º. 3. 116º. Classify PQO by its sides. Then determine if the triangle is a right triangle. Use the distance formula to find the side lengths. STEP 1. EXAMPLE 2.

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1. 90º

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  1. ~ 4. How do you know that 1 = 2? 2 1 Classify each angle as acute, obtuse, or right. 1. 90º 2. 72º 3. 116º

  2. Classify PQOby its sides. Then determine if the triangle is a right triangle. Use the distance formula to find the side lengths. STEP1 EXAMPLE 2 Example 1 (a): Found on page 208 in the book Classify a triangle in a coordinate plane

  3. Check for right angles. STEP2 EXAMPLE 2 Classify a triangle in a coordinate plane

  4. for Examples 1 and 2 Example 1 (b) GUIDED PRACTICE Triangle ABChas the vertices A(0, 0), B(3, 3), and C(–3, 3). Classify it by its sides. Then determine if it is a right triangle.

  5. Try on your own! A triangle has the given vertices. Graph the triangle and classify it By its sides. Then determine if it is a right triangle. A (2, 3), B (6, 3), C (2, 7)

  6. Important Theorems THEOREM 4.1: Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180°. THEOREM 4.2: Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

  7. FindmJKM. STEP1 Write and solve an equation to find the value of x. STEP2 Plug it in! Plug it in! Example 2 (a) Found on page 209 EXAMPLE 3 Find an angle measure

  8. More Examples of Using Triangle Angle Sum Theorem and Exterior Angle Theorem Find the value of x. Then classify the triangle by its angles. 1. 2.

  9. Find the measure of each interior angle of ABC, where mA=x , mB=2x°, and mC=3x°. 1. Find the measure of 1 in the diagram shown. ° Try these on your own! for Examples 3 and 4 GUIDED PRACTICE 2. Find the value of x and then find the measure of each angle. 3.

  10. COROLLARY Corollary: A statement that can be proved easily using a theorem. Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary.

  11. Example 3: Page 210 EXAMPLE 4 Find angle measures from a verbal description Step 1: Use the corollary to set up and solve an equation.

  12. Find the measures of the acute angles of the right triangle in the diagram shown. A 2x x Q B C Try on your own! for Examples 3 and 4 GUIDED PRACTICE What is the measure of the obtuse angle formed between the staircase and a segment extending from the horizontal leg?

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