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Section 2.2 Angles Formed by Parallel Lines Goal: Prove properties of angles formed by parallel lines and a transversal, and use these properties to solve problems. (I) Transversal Line Review of Last Day ●Corresponding Angles formed by a transversal intersecting parallel lines are congruent. Identify the angles. ___________ ___________ ___________ ___________ ●Supplementary Angles two angles that add to 180°. 1 2 ●Vertically Opposite Angles angles formed by the intersection of two lines that are opposite each other. 1 2 (II) Alternate Interior, Alternate Exterior and Interior Angles on same side of transversal. Transversal Line ●Alternate Interior Angles Two non-adjacent interior angles on opposite sides of a transversal. Identify the angles. ___________ ___________ ●Alternate Exterior Angles Two exterior angles formed between two lines and a transversal, on opposite sides of a transversal. Identify the angles. ___________ ___________ ●Same Side Interior Angles Angles formed between two lines and a transversal that lie in the interior and the same side of a transversal. Identify the angles. ___________ ___________ http://www.mathwarehouse.com/geometry/angle/interactive-transveral-angles.php (III) Transitive Property If A = B and B = C then ________________ (IV) Proving Conjectures Involving Interior Angles Formed by Parallel Lines Alternate Interior Angles In the diagram ∠1 = 120⁰ and line m and n are parallel determine the value of: ∠2 = ________ ∠1 = 120° m ∠3 n ∠3 = ________ ∠2 What do you notice about alternate interior angles? ____________________________ Make a conjecture about all alternate interior angles formed by a transversal that intersect parallel lines. _________________________________________________________________ _________________________________________________________________ Prove the conjecture based on the diagram given below. Line m∥ n Statement Justification m ∠1 ∠3 n ∠2 Alternate Exterior Angles In the diagram ∠1 = 120⁰ and line m and n are parallel determine the value of: ∠3 = ________ ∠1 = 120° m ∠3 n ∠2 = ________ ∠2 What do you notice about alternate exterior angles? ____________________________ Make a conjecture about all alternate exterior angles formed by a transversal that intersect parallel lines. _________________________________________________________________ _________________________________________________________________ Prove the conjecture based on the diagram given below. Line m∥ n Statement Justification m ∠1 ∠3 n ∠2 Same Side Interior Angles In the diagram ∠1 = 120⁰ and line m and n are parallel determine the value of: ∠2 = ________ m ∠1 = 120° ∠3 n ∠3 = ________ ∠2 What do you notice about sum of same side interior angles? ____________________________ Make a conjecture about all same side interior angles formed by a transversal that intersect parallel lines. _________________________________________________________________ _________________________________________________________________ Prove the conjecture based on the diagram given below. Line m∥ n Statement Justification m ∠1 ∠3 ∠2 n (V) Summary When a Transversal intersects parallel lines, ●corresponding angles are equal ∠___ ≅ ∠___ ∠___ ≅ ∠___ ∠___ ≅ ∠___ ∠___ ≅ ∠___ ●alternate interior angles are equal ∠___ ≅ ∠___ and ∠___ ≅ ∠___ ●alternate exterior angles are equal ∠___ ≅ ∠___ and ∠___ ≅ ∠___ ●same side interior angles are supplementary ∠___ + ∠___ = 180⁰ ∠___ + ∠___ = 180⁰ and (VI) Reasoning to Determine Unknown Angles Example: Determine the measures of: ∠a = _______ b a c ∠b = _______ ∠c = _______ ∠d = _______ d 110⁰ (VII) Using Angle Properties to Prove that Lines are Parallel Example: Use the angle measures to prove that braces CG, BF and AE are parallel. H D 78⁰ 78⁰ C G 35⁰ 78⁰ B 78⁰ A P.78 – 79 #1, #2, #3, #4, #8 35⁰ 22⁰ F 22⁰ E