WARM UP Identify each angle pair and and and and 7 Corresponding angles Alternate interior angles Alternate exterior angles Same side interior angles

PARALLEL LINES & TRANSVERSALS

OBJECTIVES  Prove and use theorems about the angles formed by parallel lines and a transversal.

KEY TERMS & CONCEPTS  Transversal  Parallel lines  Corresponding angles  Postulate  Intersection

CORRESPONDING ANGLES POSTULATE

EXAMPLE 1 Find each angle measure] A.m ECF B.m DCE x = 70 Corr. Angles Postulate m QRS = 5x m ECF = 70° 5x = 4x + 22 = 5(22) x = 22 Substitution 22 for x Corr. Angles Postulate Subtract 4x from both sides = 110°

TRY THIS… Find m QRS x = 118 Corr. Angles Postulate m QRS + x = 180° m QRS = x = 180° – x = 180° – 118° = 62° Definition of a linear pair Subtract x from each side Substitute 118° for x

HELPFUL HINT  If a transversal is perpendicular to two parallel lines, all eight angles are congruent

DEFINITIONS  Postulates are statements that are accepted without proof.  Corresponding angles are created where a transversal crosses other (usually parallel lines) lines. They are the ones at the same location at each intersection.

EXAMPLE 2 Find each angle measure A.m EDG B.m BDG x = 105 m EDG = 75° m BDG = 105° x – 30° = 75° Alt. Ext. Angles Theorem Add 30 to both sides

TRY THIS… Find m ABD x = 25 2x + 10° = 3x – 15° m ABD = 2(25) + 10 = 60° Alt. Ext. Angles Theorem Subtract x from both sides Substitute 25 for x

MUSIC APPLICATION Find x and y in the diagram. By the Alternate Interior Angles Theorem, (5x + 4y)° = 55° By the Corresponding Angles Postulate, (5x + 5y)° = 60° 5x + 5y = 60 –(5x + 4y = 55) y = 5 Subtract the first equation from the second equation. 5x + 5(5) = 60 Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x. x = 7, y = 5

TRY THIS… Find the measures of the acute angles in the diagram. By the Alternate Exterior Angles Theorem, (25x + 5y)° = 125° By the Corresponding Angles Postulate, (25x + 4y)° = 120° An acute angle will be 180° – 125°, or 55°. The other acute angle will be 180° – 120°, or 60°.

HOMEWORK Textbook pg. 158 # 2, 4, 8, 10, 12 & 16 Journal Question #1: Answer the following question in a minimum of one paragraph (4 sentences) and submit via DP.net. “Explain why a transversal that is perpendicular to two parallel lines forms eight congruent angles.”