Angle Theorems

Question 1

What are vertically opposite angles?

Answer 1

They are angles that have the same vertex and are not adjacent to each other.

Question 2

Theorem 1

Answer 2

vertically opposite angles are equal in measure

Question 3

What is a transversal

Answer 3

A line cuts two or more lines is called a transversal.

Question 4

What is an alternate angle

Answer 4

Alternate angles are on opposite sides of the transversal that cuts two lines but are between the two lines.
If two lines are parallel, then the alternate angles formed by a transversal are equal.

Question 5

Theorem 3

Answer 5

If a transversal makes equal alternative angles on two lines then the lines are parallel (and converse).

Question 6

What are corresponding angles?

Answer 6

Corresponding angles are on the same side of the transversal that cuts two lines. One angle is between the lines, and the other angle is outside the lines. (makes an F shape)

Question 7

Theorem 5

Answer 7

Two lines are parallel if and only if, for any transversal, corresponding angles are equal.

Question 8

Theorem 6

Answer 8

Each exterior angle of a triangle is equal to the sum of the interior opposite angles.

Question 9

Theorem 4

Answer 9

The angles in any triangle sum to 180 degrees.