1. GEOMETRY HELP m ACB = 90 Definition of right angle Find c first, using the fact that ACB is a right angle. c + 70 = 90 Angle Addition Postulate c = 20 Subtract 70 from each side. Parallel Lines and the Triangle Angle-Sum Theorem LESSON 3-4 Additional Examples In triangle ABC, ACB is a right angle, and CD AB. Find the values of a, b, and c.

2. GEOMETRY HELP a + m ADC + c = 180Triangle Angle-Sum Theorem m ADC = 90Definition of perpendicular lines a + 90 + 20 = 180Substitute 90 for m ADC and 20 for c. a + 110 = 180Simplify. a = 70Subtract 110 from each side. 70 + m CDB + b = 180 Triangle Angle-Sum Theorem m CDB = 90 Definition of perpendicular lines 70 + 90 + b = 180 Substitute 90 for m CDB. 160 + b = 180 Simplify. b = 20 Subtract 160 from each side. To find b, use CDB. To find a, use ADC. (continued) Quick Check Parallel Lines and the Triangle Angle-Sum Theorem LESSON 3-4 Additional Examples

3. GEOMETRY HELP The three sides of the triangle have three different lengths, so the triangle is scalene. One angle has a measure greater than 90, so the triangle is obtuse. The triangle is an obtuse scalene triangle. Classify the triangle by its sides and its angles. Quick Check Parallel Lines and the Triangle Angle-Sum Theorem LESSON 3-4 Additional Examples

4. GEOMETRY HELP Find m  1. m  1 + 90 = 125Exterior Angle Theorem m  1 = 35Subtract 90 from each side. Parallel Lines and the Triangle Angle-Sum Theorem LESSON 3-4 Additional Examples Quick Check

5. GEOMETRY HELP Explain what happens to the angle formed by the back of the chair and the armrest as you make a lounge chair recline more. The exterior angle and the angle formed by the back of the chair and the armrest are adjacent angles, which together form a straight angle. As one measure increases, the other measure decreases. The angle formed by the back of the chair and the armrest increases as you lower the back of the lounge chair. Parallel Lines and the Triangle Angle-Sum Theorem LESSON 3-4 Additional Examples Quick Check