3-2 Angles and Parallel Lines You named angle pairs formed by parallel lines and transversals. Use theorems to determine the relationships between specific pairs of angles. Use algebra to find angle measurements. Page 180
Parallel Crossing You will need a sheet of paper, a straightedge and a protractor. Draw two parallel lines. Draw a transversal through the two lines. Measure all the angles. Do you see any patterns?
Postulate 3.1 p. 181 If parallel lines are cut by a transversal, then the Corresponding Angles are congruent.
Page 180
A. In the figure, m11 = 51. Find m15 A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used. 15 11 Corresponding Angles Postulate m15 = m11 Definition of congruent angles m15 = 51 Substitution Answer: m15 = 51
B. In the figure, m11 = 51. Find m16 B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used. 16 15 Vertical Angles Theorem 15 11 Corresponding Angles Postulate 16 11 Transitive Property () m16 = m11 Definition of congruent angles m16 = 51 Substitution Answer: m16 = 51
A. In the figure, a || b and m18 = 42. Find m22. C. 48 D. 138
A. In the figure, a || b and m18 = 42. Find m22. C. 48 D. 138
Alternate Interior Angles Theorem If parallel lines are cut by a transversal, then the Alternate Interior angles are congruent. x x x x
Page 181
FLOOR TILES The diagram represents the floor tiles in Michelle’s house FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3. 2 3 Alternate Interior Angles Theorem m2 = m3 Definition of congruent angles 125 = m3 Substitution Answer: m3 = 125
FLOOR TILES The diagram represents the floor tiles in Michelle’s house FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4. A. 25 B. 55 C. 70 D. 125
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. 5 7 Corresponding Angles Postulate m5 = m7 Definition of congruent angles 2x – 10 = x + 15 Substitution x – 10 = 15 Subtract x from each side. x = 25 Add 10 to each side. Answer: x = 25
Theorems If parallel lines are cut by a transversal, then Consecutive Interior angles are supplementary.
Theorems If parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
Page 181
What special relationships happen when a transversal crosses parallel lines? If parallel lines are cut by a transversal, then the alternate interior angles are congruent. If parallel lines are cut by a transversal, then the corresponding angles are congruent. If parallel lines are cut by a transversal, then the alternate exterior angles are congruent. If parallel lines are cut by a transversal, then same-side interior angles are supplementary.
This is a special relationship that exists when the transversal of two parallel lines is a perpendicular line. Page 182
3-2 Assignment p. 183, 11-19, 24-28