Warm-Up Exercises 1.90º 2. 72º Classify each angle as acute, obtuse, or right. 3.116º 4. How do you know that 1 = 2? ~ 2 1.

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Presentation transcript:

Warm-Up Exercises 1.90º 2. 72º Classify each angle as acute, obtuse, or right º 4. How do you know that 1 = 2? ~ 2 1

Warm-Up Exercises EXAMPLE 2 Classify a triangle in a coordinate plane STEP 1 Use the distance formula to find the side lengths. Classify PQO by its sides. Then determine if the triangle is a right triangle. Example 1 (a): Found on page 208 in the book

Warm-Up Exercises EXAMPLE 2 Classify a triangle in a coordinate plane STEP 2 Check for right angles.

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Triangle ABC has 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. Example 1 (b)

Warm-Up Exercises 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)

Warm-Up Exercises 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.

Warm-Up Exercises EXAMPLE 3 Find an angle measure STEP 1 Write and solve an equation to find the value of x. STEP 2 Plug it in! Find m  JKM. Example 2 (a) Found on page 209

Warm-Up Exercises More Examples of Using Triangle Angle Sum Theorem and Exterior Angle Theorem Find the value of x. Then classify the triangle by its angles

Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 1. Find the measure of 1 in the diagram shown. 2. Find the value of x and then find the measure of each angle. Try these on your own! Find the measure of each interior angle of ABC, where m A = x, m B = 2x °, and m C = 3x °. ° 3.

Warm-Up Exercises 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.

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

Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 Find the measures of the acute angles of the right triangle in the diagram shown. Try on your own! What is the measure of the obtuse angle formed between the staircase and a segment extending from the horizontal leg? A B C Q 2x2x x