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Learn about parallel lines and congruent angles, including the Parallel Postulate and the six theorems associated with parallel lines and transversals. Practice solving angle equations and applying postulates and theorems to geometric figures.
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Lesson 5.3 Congruent Angles Associated with Parallel Lines
Most Theorems in this section are converses of what we learned in sec 5-2 • In this section we start with parallel lines then state the special pairs of angles
Parallel Postulate: Through a point not on a line, there is exactly one parallel to the given line. P a
Notice the special tick marks ( ) used to designate parallel lines.
If two parallel lines are cut by a transversal, then • Each pair of alternate interior angles are congruent • Each pair of alternate exterior angles are congruent • Each pair of corresponding angles are congruent • Each pair of interior angles on the same side of the transversal are supplementary • Each pair of exterior angles on the same side of the transversal are supplementary.
Solve Since alt. int. s are , 3x + 5 = 2x + 10 x + 5 = 10 x = 5 3(5) + 5 = 20 Because vertical s are , m1 = 20.
Given ║ lines → alt. int. s Given Given Addition Property (BC to step 4) SAS (3, 2, 5) CPCTC FA ║ DE A D FA DE AB CD AC BD ΔFAC ΔEDB F E
5 4 m 3 2 Using the Parallel Postulate, draw m parallel to a. 2 & 3 are congruent (alt. int. s are ) 3 = 40° 4 & 5 are supplementary. 4 = 80° 1 = 40° + 80° = 120°
PAI • PAE • PCA • PSSIS • PSSES • 2P3P • Dual ̸̸ ̸ theorem • Dual ⊥ theorem