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8.3 Angle Relationships

8.3 Angle Relationships. 1. 2. Angle Relationships. Adjacent angles have a common vertex and a common side, but no common interior points. (They’re NEXT to each other and NOT necessarily supplementary). Writing Math. ~. The symbol for congruence is =, which is read as “is congruent to.”.

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8.3 Angle Relationships

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  1. 8.3 AngleRelationships

  2. 1 2 Angle Relationships Adjacent angles have a common vertex and a common side, but no common interior points. (They’re NEXT to each other and NOT necessarily supplementary)

  3. Writing Math ~ The symbol for congruence is =, which is read as “is congruent to.” So m1 = m3, or 1 3. Finding Angle Measures Use the diagram to find each angle measure. A. If m1 = 37°, find m3. 1 and 2 are supplementary. m2 = 180° – 37° = 143° The measures of 2 and 3 are supplementary. m3 = 180° – 143° = 37°

  4. 1 2 4 3 Parallel and Perpendicular Lines Intersecting Lines form Two Pair of Congruent Vertical Angles Vertical angles are the nonadjacent angles formed by two intersecting lines. (They’re OPPOSITE each other).

  5. A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angle pairs with special properties. 1 2 4 3 5 6 8 7 Alternate Interior Angles: Opposite side of the transversal Inside the parallel lines

  6. 1 2 3 4 5 6 8 7 Alternate Exterior Angles: Opposite side of the transversal Outside the parallel lines

  7. 1 2 4 3 5 6 8 7 Corresponding Angles: Same side of the transversal One inside and one outside the parallel lines

  8. 1 2 4 3 5 6 8 7 Vertical Vertical Angles: Non-adjacent angles (Angles across from each other)

  9. 1 2 4 3 5 6 8 7 Supplementary Supplementary Angles: Angles that add to 180 degrees

  10. Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. A. 4 Corresponding angles are congruent. m4 = 124°

  11. 144° 1 m 4 3 6 5 n 8 7 Check It Out! In the figure, line l|| line m. Find the measure of the angle. Alternate exterior angles are congruent. A. 7 m7 = 144°

  12. 144° 1 m 4 3 6 5 n 8 7 –144° –144° Check It Out! In the figure, line l|| line m. Find the measure of the angle. B. 1 1 is supplementary to the 144° angle. m1 + 144° = 180° m1 = 36°

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