Geometry Theorems and Postulates

Postulate 1-6

The ___ ___ postulate states if three points are collinear then their segments add up to the total length of the line segment. I.E. AB + BC = AC

Postulate 1-8

The ___ ___ postulate states that the measurements of the interior angles of the whole angle can be added together to find the total measurement.

Postulate 1-9

If two angles form a linear pair, then they are ___.

Which of the following theorems would verify that ∠COB & ∠AOD are congruent?

• Straight Angle Theorem

• Congruent Angle Theorem

• Vertical Angles Theorem

• Linear Pair Theorem

• They are supplementary by same side interior angles postulate (3-1).

• They are supplementary by same side interior angles converse (Thm 3-6).

• They are congruent by corresponding angles converse (Thm 3-4).

• They are congruent by corresponding angles theorem (3-2).

Alternate Exterior Angles Theorem (3-3)

• If a pair of parallel lines is cut by a traversal, then alternate exterior angles are congruent.

• If a pair of parallel lines is cut by a traversal, then alternate exterior angles are supplementary.

• If alternate exterior angles are congruent, then a pair of parallel lines is cut by a traversal.

• If alternate exterior angles are supplementary, then a pair of parallel lines is cut by a traversal.

Post. 3-1: Same Side Angle Post.

When parallel lines are intersected by a transversal, Same Side Interior angles...

• are supplementary.

• are congruent.

• are complementary.

• are straight angles.

In the Alternate Interior Angle Theorem (3-1), for alternate interior angles to be congruent...

• The transversal has to cut through two lines

• Alternate Interior Angles are always congruent

• The transversal has to cut through two parallel lines

• All lines have to be parallel

Which theorem explains why the two lines are parallel?

• Alt. Exterior Angles Thm (3-3)

• Same Side Int. Angles Post (3-1)

• Alt. Exterior Angles Converse (Thm 3-7)

• Same Side Int. Angles Converse (Thm 3-6)

Which theorem explains why the two lines are parallel?

• Corresponding Angles Converse (Thm 3-4)

• Alt. Interior Angles Converse (Thm 3-5)

• Corresponding Angle Thm (3-2)

• Alt. Interior Angles Thm (3-1)