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Transversals and Parallel Lines
Mod 14.2: Transversals and Parallel Lines Essential Question: How can you prove and use theorems about angles formed by transversals that intersect parallel lines? CASS: G-CO.9 Prove theorems about lines and angles. MP.3 Logic
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Transversal Transversal is a line that intersects two or more coplanar lines at two different points.
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A transversal is a line that intersects two or more coplanar lines at different points.
1 2 3 4 5 6 7 8 t t 2 1 4 3 5 6 7 8 corresponding angles “same location” 1 & 5 are 1 & 8 are alternate exterior angles
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alternate interior angles 3 & 5 are
1 2 3 4 5 6 7 8 t 1 2 3 4 5 6 7 8 t 3 & 6 are alternate interior angles 3 & 5 are Same side interior angles
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Identifying Angle Relationships
EXAMPLE 1 Identifying Angle Relationships List all angle pairs that fit the description. 4 3 2 1 8 7 a. corresponding 6 5 b. alternate interior d. vertical c. same side interior
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SAME SIDE INTERIOR ANGLES POSTULATE
If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary. 7 8 ALTERNATE INTERIOR ANGLES THEOREM If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 3 4
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ALTERNATE EXTERIOR ANGLES THEOREM
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. 1 8 CORRESPONDING ANGLES THEOREM If two parallel lines are cut by a transversal, then corresponding angles are congruent. 1 2
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Find Missing Angle Measures
EXAMPLE 2 Find Missing Angle Measures Given that m∠ 1 = 75°, find each measure and explain your reasoning. 3 1 5 6 7 8 4 2 a. m∠ 3 105°; Linear Pair Postulate b. m∠ 8 75°; Corresponding Angles Postulate c. m∠ 5 75°; Vertical Angles are congruent d. m∠ 4 75°; Vertical angles are congruent
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Use properties of parallel lines to find the value of x.
TRY THIS Use properties of parallel lines to find the value of x. 1 Vertical angles are congruent Same side Interior Angles Postulate Substitute
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TRY THIS a b 1 2 5 6 If a||b and c||d and m∠ 2 = 99°; find each measure below and explain your reasoning 3 4 7 8 c 9 10 13 14 d 11 12 15 16 m∠ 4 = 81° m∠ 7 = 99° m∠ 11 = 99° m∠ 5 = 81° m∠ 16 = 81°
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Using Properties of Parallel Lines
EXAMPLE 3 Using Properties of Parallel Lines Use properties of parallel lines to find the value of x.
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pp. 694 #1-14 all Key Content: ASSIGNMENTS Parallel Lines Transversal
Same-Side Interior Angles Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Same-Side Interior Angles Postulate Corresponding Angles Theorem Alternate Interior Angles Theorem Alternate Exterior Angles Theorem
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