Angles formed by parallel lines cut by transversal
- 1. ANGLES FORMED BY PARALLEL LINES CUT BY TRANSVERSAL 8/28/2012 1 MAY P. BUNDANG ZNHS
- 2. tt t SET A t is a transversal t t t SET B t is not a transversal
- 3. Transversal is a line that intersects two or more lines at different points
- 4. If parallel lines are cut by a transversal, then eight angles and pairs of angle are formed. 1 2 l 5 4 3 n 7 8 6 m l and m are parallel lines (l // m) n is a transversal
- 5. Corresponding angles – a combination of an exterior angle and an interior angle which are non-adjacent but lie on the same side of the transversal 1 2 l 5 4 3 n 7 8 6 m
- 6. • Interior angles on the same side of the transversal 1 2 l 5 4 3 n 7 8 6 m Interior angles 1 2 l 5 4 3 n 7 8 6 m • Alternate interior angles
- 7. • Exterior angles on the same side of the transversal 1 2 l 5 4 3 n 7 8 6 m Exterior angles 2 l 5 4 3 n 7 8 6 m • Alternate exterior angles
- 8. Observe the measures of the angle pairs. n 1 2 l 5 4 3 7 8 6 m 110o 70o 110o 110o 110o 70o 70o 70o
- 9. Pairs of Angles Measurement •Corresponding Angles 1 and 5 4 and 7 2 and 6 3 and 8 110 o 70o 70o 110 o •Alternate interior angles 3 and 5 4 and 6 110 o 70o •Interior angles on the same side of the transversal 4 and 5 3 and 6 4 = 70 o and 5 = 110o 6 = 70 o and 3 = 110o •Alternate exterior angles 1 and 8 2 and 7 110 o 70o •Interior angles on the same side of the transversal 1 and 7 2 and 8 1= 110 o and 7 = 70o 8= 110 o and 2 = 70o
- 10. What did you observe with the measurements of the pairs of angles? a. Corresponding angles? b. Alternate interior angles? c. Interior angles on the same side of the transversal? d. Alternate exterior angles? e. exterior angles on the same side of the transversal?
- 11. Answers: • Corresponding angles are congruent. • Alternate interior angles are congruent. • Interior angles on the same side of the transversal are supplementary. • Alternate exterior angles are congruent. • Exterior angles on the same side of the transversal are supplementary.
- 12. Given: l // m n 1 11 l 5 43 78 6 m p 2 10 16 13 12 9 15 14 1. Find the measure of the other numbered angles, if measure of a. 1 is 68o b. 3 is 95o
- 13. 2. If measure of 6 = 5x – 10 and measure of 3 = 8x - 34, a. what is x? b. find the measure of the angles. r 21 s f43 7 8 65
- 14. Conclusion: If two lines are cut by a transversal then • corresponding angles are congruent. • alternate interior angles are congruent. • interior angles on the same side of the transversal are supplementary. • alternate exterior angles are congruent. • exterior angles on the same side of the transversal are supplementary.
- 15. 2. If measure of 2 = x + 20 and measure of 5 = 4x - 50, a. what is x? b. find the measure of the angles.
- 16. 4x + 15 n 1 11 l 5 43 78 6 m p 2 10 16 13 12 9 15 14 3X - 20 X + 40 6X - 25 3. Solve for x and find the measure of the angles.