congruent angles associated with parallel lines. parallel postulate: through a point not on a line,...
TRANSCRIPT
Lesson 5.3
Congruent Angles Associated with Parallel
Lines
Parallel Postulate: Through a point not on a line, there is exactly one parallel to the given line.
a
P
Notice the special tick marks ( ) used to designate parallel lines.
Six Theorems About 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 = 20Because vertical s are , m1 = 20.
1.FA ║ DE2. A D3.FA DE4.AB CD5.AC BD6.ΔFAC ΔEDB7. F E
1.Given2.║ lines → alt. int. s 3.Given4.Given5.Addition Property (BC to
step 4)
6.SAS (3, 2, 5)
7.CPCTC
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°
m4
3
2
5