LESSON 3.5SECTIONS 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