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MWA 10 5.4 Angles and Parallel Lines
- 1. Parallel Lines andthe Angles Formed Slide 1 Vertically opposite angles are equal. Corresponding angles are equal. Same-side interior angles are supplementary (adds up to 180). Alternate interior angles are equal. Same-side exterior angles are supplementary (adds up to 180). Alternate exterior angles are equal.
- 2. Slide 2 Example 1: Inthe diagram below, l1 is parallel to l2. State the measures of the indicated angles and explain your reasoning.
- 3. Slide 3 Example 1: Inthe diagram below, l1 is parallel to l2. State the measures of the indicated angles and explain your reasoning. Lines 1 and 2 are parallel (given). 2 and 118 are supplementary 2 + 118 = 180 2 = 62 > >
- 4. Slide 4 Example 1: Inthe diagram below, l1 is parallel to l2. State the measures of the indicated angles and explain your reasoning. Lines 1 and 2 are parallel (given). 2 and 118 are supplementary 2 + 118 = 180 2 = 62 3 and 118 are corresponding angles so they are equal 3 = 118 > >62
- 5. Slide 5 Example 1: Inthe diagram below, l1 is parallel to l2. State the measures of the indicated angles and explain your reasoning. Lines 1 and 2 are parallel (given). 2 and 118 are supplementary 2 + 118 = 180 2 = 62 3 and 118 are corresponding angles so they are equal 3 = 118 1 and 71 are same-side interior angles so they are supplementary (adds up to 180) 1 + 71 = 180 1 = 109 > >62 118
- 6. Slide 6 Example 1: Inthe diagram below, l1 is parallel to l2. State the measures of the indicated angles and explain your reasoning. Lines 1 and 2 are parallel (given). 2 and 118 are supplementary 2 + 118 = 180 2 = 62 3 and 118 are corresponding angles so they are equal 3 = 118 3 and 4 are supplementary 3 + 4 = 180 118 + 4 = 180 4 = 62 OR (alternate solution) 2 and 4 are corresponding 2 = 4 = 62 1 and 71 are same-side interior angles so they are supplementary (adds up to 180) 1 + 71 = 180 1 = 109 > >62 118 109
- 7. Slide 7 Example 1: Inthe diagram below, l1 is parallel to l2. State the measures of the indicated angles and explain your reasoning. Lines 1 and 2 are parallel (given). 2 and 118 are supplementary 2 + 118 = 180 2 = 62 3 and 118 are corresponding angles so they are equal 3 = 118 3 and 4 are supplementary 3 + 4 = 180 118 + 4 = 180 4 = 62 OR (alternate solution) 2 and 4 are corresponding 2 = 4 = 62 1 and 71 are same-side interior angles so they are supplementary (adds up to 180) 1 + 71 = 180 1 = 109 > >62 118 109 62
- 8. Slide 8 Example 2: Aplumber must install pipe 2 parallel to pipe 1. He knows that 1 is 53. What is the measure of 2?
- 9. Slide 9 Example 2: Aplumber must install pipe 2 parallel to pipe 1. He knows that 1 is 53. What is the measure of 2? Pipes 1 and 2 are to be parallel (given) 1 and 2 are same-side interior angles Same-side interior angles are supplementary 1 + 2 = 180 53 + 2 = 180 2 = 127 Angle 1 is 53 (given) In order for pipes 1 and 2 to be parallel, the measure of 2 should be 127 > > 53