Download 3.5 Vertical Angles and Parallel Lines

LESSON 3.5
SECTIONS 5.5.1 AND 5.5.2 (PAGES 126-149)
Proving Theorems about
Lines and Angles
Let’s review some ideas about angles:
•Angles can be labeled with one point at the vertex, three points with the vertex point in
the middle, or with numbers. See the examples that follow.
Straight angles are angles with rays in opposite directions—in
other words, straight angles are straight lines.
•
• Adjacent angles are angles that lie in the same plane and share
a vertex and a common side. They have no common interior points.
Linear pairs are pairs of adjacent angles whose non-shared sides form a straight angle.
Vertical Angles Theorem :
Vertical angles are congruent
Supplementary angles are two angles whose sum is 180º.
• Supplementary angles can form a linear pair or be nonadjacent.
Complementary angles are two angles whose sum is 90º.
Example 1 (page 127)
Look at the following diagram. List pairs of supplementary angles, pairs of vertical angles,
and a pair of opposite rays.
Example 3 (page 128):
Corresponding Angles Postulate (page 140)
If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Alternate Interior Angles Theorem
If two parallel lines are intersected by a
transversal, then alternate interior angles
are congruent.
Same-Side Interior Angles Theorem
If two parallel lines are intersected by a
transversal, then same-side interior angles
are supplementary.
Alternate Exterior Angles Theorem
If parallel lines are intersected by a
transversal, then alternate exterior
angles are congruent.
Same-Side Exterior Angles Theorem
If two parallel lines are intersected by a
transversal, then same-side exterior angles
are supplementary.
Example 3 (page 143):
ASSIGNMENT 3.5
 WB:
• Page 133 #’s 1-8
• Page 147 #’s 1-5, 8
RB:
• Page U5-167 #8