4.2 Transversals and Parallel Lines

4.2 Transversals and Parallel Lines

4.2 Transversals and Parallel Lines Pgs. 26, 28, 30 Warmup (pg. 23) 1.The measures of 2 Vertical Angles are 90 and (5x + 10). Find the value of x. 2.The measure of an angle is twice the measure of its compliment. Whats a Transversal?

A transversal is a line that intersects two coplanar lines at two different points. transversal 1 2 p 4 3 5 6 8 7

q Angle Pairs Formed by the Transversal Corresponding Angles Same side of trans & intersecting lines Exs: 1 & 5 2 & 6 Same Side Interior Angles (SSI)

Same side of the trans, and inside the lines Exs: 4 & 5 3 & 6 Same Side Exterior Angles (SSE) Same side of the

Exs: trans, and outside the 1 & 8 lines 2 & 7 Alternate Interior Angles (AIA) Opposite nonadjacent angles on the inside of lines Exs: 3 & 5

4 & 6 Alternate Exterior Angles (AEA) Opposite nonadjacent angles on the outside of lines Exs: 1 & 7 2 & 8 4 & 8

3 & 7 Parallel Lines 2 lines that never meet When parallel lines are cut by a transversal, the angle pairs formed are either congruent or supplementary. Same Side Interior Postulate If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary.

Ex: m4 = 30. Find m5. m5 + 30 = 180 - 30 m5 -30 = 150 m5 = 150 *Postulate can be applied to Same Side Exterior Angles too Alternate Interior Angles Postulate If two parallel lines are cut by a transversal, then the pairs of Alternate

Interior Angles are congruent. *Postulate can be applied to Alternate Exterior Angles too Proof: 1. p // q 1. Given 2. 3 & 6 are supp. 2. Same Side Interior Angles

3. 5 & 6 are LP 3. From pic/ given 4. m3 + m6 = 180 4. Def of Supp. 5. m5 + m6 = 180 6. m3 + m6 = m5 + m6

7. m3 = m5 5. Def. of LP 6. Transitive P.o.E. 7. Subtraction P.o.E. Corresponding Angles Theorem If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Proof: 1. p // q

1. Given 2. 4 & 6 are AIA 2. From pic/given 3. m4 = m6 3. AIA Postulate 4. 6 & 8 are VA

4. From pic/given 5. m6 = m8 5. VA Thm 6. m4 = m8 6. Substitution P.o.E. Examples Examples

Examples Examples

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