1.6 What you should learn Why you should learn it

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Presentation transcript:

1.6 What you should learn Why you should learn it Angle Pair Relationships What you should learn GOAL 1 Identify vertical angles and linear pairs. GOAL 2 Identify complementary and supplementary angles. Why you should learn it To solve real-life problems, such as finding the measures of angles formed by the cables of a bridge.

1.6 Angle Pair Relationships 1 GOAL VERTICAL ANGLES AND LINEAR PAIRS Vocabulary Two angles whose sides form two pairs of opposite rays are called _____________. vertical angles Identify the pairs of vertical angles in the diagram. Click to check. 1 4 2 3

Two adjacent angles whose noncommon sides are opposite rays are called a _________. linear pair 5 6 common side noncommon sides are a linear pair. EXAMPLE 1

Extra Example 1 1 5 4 3 2 Are a linear pair? b. Are a linear pair? c. Are vertical angles? d. Are vertical angles? Click to see the answers. yes no no yes EXAMPLE 2

Extra Example 2 In one town, Main Street and Columbus Avenue intersect to form an angle of 36°. Find the measures of the other three angles. Click to see a diagram. Columbus Avenue Main Street 36° Click to see the answers. EXAMPLE 3

Extra Example 3 Solve for x and y. Then find the angle measures. Click for a hint. L M P N O Solve each equation to find x and y. Click for the answers.

Checkpoint 1. Name one pair of vertical angles and one pair of angles that form a linear pair. Click to see the answers. J H K G I Vertical angle pairs: Linear pairs: 2. What is the measure of

1.6 Angle Pair Relationships 2 COMPLEMENTARY AND SUPPLEMENTARY ANGLES GOAL 2 COMPLEMENTARY AND SUPPLEMENTARY ANGLES Vocabulary If the sum of the measures of two angles is 90°, the angles are ______________ angles, and each is the ___________ of the other. complementary complement are now nonadjacent complementary angles. 1 Note: Complementary angles may or may not be adjacent. 2

Note: Supplementary angles may or may not be adjacent. If the sum of the measures of two angles is 180°, the angles are _____________ angles, and each is the ___________ of the other. supplementary supplement Note: Supplementary angles may or may not be adjacent. If are adjacent and supplementary, they form a _________. linear pair 3 4 are now nonadjacent supplementary angles, and they no longer form a linear pair. EXAMPLE 4

Extra Example 4 State whether the two angles are complementary, supplementary, or neither. Click for the solution. 12 12 neither supplementary 9 3 9 3 neither 6 6 EXAMPLE 5

Extra Example 5 Given that is a supplement of find Click to see the solution. Given that is a complement of find Click to see the solution. EXAMPLE 6

Substitute and solve. Click for the solution. Extra Example 6 are supplementary. The measure of is half the measure of Find Click for a hint. Substitute and solve. Click for the solution.

Substitute and solve. Click for the answers. Checkpoint are complements and are supplements. If is four times find the measure of each of the three angles. Click for a hint. Substitute and solve. Click for the answers.

QUESTIONS?