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4.2 Transversals and Parallel Lines. Pgs. 26, 28, 30. Warmup (pg. 23). The measures of 2 Vertical Angles are 90 and (5x + 10). Find the value of x. The measure of an angle is twice the measure of its compliment. What’s a Transversal?.
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4.2 Transversals and Parallel Lines Pgs. 26, 28, 30
Warmup (pg. 23) • The measures of 2 Vertical Angles are 90 and (5x + 10). Find the value of x. • The measure of an angle is twice the measure of its compliment.
What’s a Transversal? A transversal is a line that intersects two coplanar lines at two different points. transversal 1 2 4 3 p 5 6 8 7 q
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: m∠4 = 30°. Find m∠5. m∠5 + 30 = 180 - 30 -30 m∠5 = 150 m∠5 = 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. m∠3 + m∠6 = 180 4. Def of Supp. 5. m∠5 + m∠6 = 180 5. Def. of LP 6. m∠3 + m∠6 = m∠5 + m∠6 6. Transitive P.o.E. 7. m∠3 = m∠5 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. m∠4 = m∠6 3. AIA Postulate 4. ∠6 & ∠8 are VA 4. From pic/given 5. m∠6 = m∠8 5. VA Thm 6. m∠4 = m∠8 6. Substitution P.o.E.
