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Lesson Menu Five-Minute Check (over Chapter 10) Then/Now New Vocabulary Key Concept: Pairs of Angles Example 1: Find a Missing Angle Measure Key Concept: Names of Special Angles Example 2: Find Measures of Angles Formed by Parallel Lines Example 3: Use Algebra to Find Missing Angle Measures

Over Chapter 10 5-Minute Check 1 A.5 B.6 C.7 D.8

Over Chapter 10 5-Minute Check 2 Which list of numbers is correctly ordered least to greatest? A. B. C. D.

Over Chapter 10 5-Minute Check 3 A.10.5 units B.10.8 units C.11.3 units D.12 units If c is the measure of the hypotenuse and a = 6 and b = 9, find the measure of c. Round to the nearest tenth.

Over Chapter 10 5-Minute Check 4 A.8.2 units B.8.1 units C.8.0 units D.7.9 units Find the distance between A(–3, 4), and B(5, 2). Round to the nearest tenth.

Over Chapter 10 5-Minute Check 5 A.102°; obtuse scalene B.92°; acute scalene C.90°; right scalene D.82°; acute scalene What is the value of x? Classify the triangle by its angles and by its sides.

Then/Now You have already found the missing angle measure of a triangle. (Lesson 10–3) Examine relationships between pairs of angles. Examine relationships of angles formed by parallel lines and a transversal.

Vocabulary perpendicular lines vertical angles adjacent angles complementary angles supplementary angles parallel lines transversal alternate interior angles alternate exterior angles corresponding angles

Concept A

Example 1 A Find a Missing Angle Measure A. Jun is cutting a tile. Classify the relationship of  a and  b. Answer: The angles are complementary. The sum of their measures is 90°.

Example 1 B Find a Missing Angle Measure B. If m  a = 53°, what is the measure of  b? m  b + 53 = 90Write the equation. m  b + 53 – 53 = 90 – 53Subtract 53 from each side. m  b = 37Simplify. Answer: m  b = 37°

Example 1 CYP A A.They are complementary. B.They are supplementary. C.They are congruent. D.They are obtuse. A. Elisa is cutting a piece of fabric. What is the relationship between  a and  b? a b

Example 1 CYP B A.140° B.220° C.50° D.90° B. If m  a = 40°, what is m  b? a b

Concept B

Example 2 A Find Measures of Angles Formed by Parallel Lines Answer: Since  9 and  13 are corresponding angles, they are congruent. A. Classify the relationship between  9 and  13.

Example 2 Find Measures of Angles Formed by Parallel Lines Answer: m  11 = 75° and m  15 = 75° B. If m  13 is 75°, find m  11 and m  15. Since  13 and  11 are alternate interior angles, they are congruent. So, m  11 = 75°.  11 and  15 are corresponding angles and are congruent. So, m  15 = 75°.

Example 2 CYP A A.They are corresponding and congruent. B.They are adjacent and supplementary. C.They are corresponding and supplementary. D.They are adjacent and congruent. A. What is the relationship between  1 and  5?

Example 2 CYP B A.12° B.22° C.78° D.102° B. If m  3 = 78°, what is m  7?

Example 3 Use Algebra to Find Missing Angle Measures ALGEBRA Angles DEF and WXY are complementary angles, with m  DEF = 2x and m  WXY = 3x – 20. Find the measures of  DEF and  WXY. m  DEF + m  WXY = 90Complementary angles 2x + 3x – 20 = 90Replace m  DEF with 2x and m  WXY with 3x – 20. Step 1 Find the value of x.

Example 3 Use Algebra to Find Missing Angle Measures Combine like terms. Add 20 to each side. Simplify. Divide each side by 5. Simplify.

Example 3 Use Algebra to Find Missing Angle Measures Answer: m  DEF = 44° and m  WXY = 46° Step 2 Replace x with 22 to find the measure of each angle. m  DEF = 2xm  WXY = 3x – 20 = 2(22) or 44 = 3(22) – 20 or 46

Example 3 A.m  ABC = 12° and m  RST = 78° B.m  ABC = 20° and m  RST = 70° C.m  ABC = 30° and m  RST = 60° D.m  ABC = 30° and m  RST = 70° Angles RST and ABC are complementary angles with m  RST = 3x and m  ABC = x What are the measures of  ABC and  RST?

End of the Lesson