warm-up exercises 1.90º 2. 72º classify each angle as acute, obtuse, or right. 3.116º 4. how do...

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

Warm-Up ExercisesEXAMPLE 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 ExercisesEXAMPLE 2 Classify a triangle in a coordinate plane

STEP 2 Check for right angles.

Warm-Up ExercisesGUIDED PRACTICEfor 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 ExercisesTry 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 ExercisesImportant Theorems

THEOREM 4.1: Triangle Sum TheoremThe sum of the measures of the interior angles of a triangle is 180°.

THEOREM 4.2: Exterior Angle TheoremThe measure of an exterior angle of a triangle is equal to the sum of the measures of the twononadjacent interior angles.

Warm-Up ExercisesEXAMPLE 3 Find an angle measure

STEP 1 Write and solve an equation to find the value of x.

STEP 2Plug it in! Plug it in!

Find mJKM.

Example 2 (a) Found on page 209

Warm-Up ExercisesMore 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.

Warm-Up ExercisesGUIDED 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 ExercisesCOROLLARY

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 ExercisesEXAMPLE 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 ExercisesGUIDED 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

2x

x