## Complementary, Supplementary, and Congruent

-Complementary angles are two angles whose measure add up to 90 degrees.

-Supplementary angles are two angles whose measure add up to 180 degrees.

-Vertical Angles are two angles whose sides form opposite rays.

-Adjacent Angles are two angles sharing a ray and vertex as a side.

-Perpendicular Pair is a pair of adjacent angles whose non-common sides form a right angle.

-Linear Pair is a pair of adjacent angles whose non-common sides form a line.

-Consecutive Angles are angles sharing a side, but having different vertices.

-Supplementary angles are two angles whose measure add up to 180 degrees.

-Vertical Angles are two angles whose sides form opposite rays.

-Adjacent Angles are two angles sharing a ray and vertex as a side.

-Perpendicular Pair is a pair of adjacent angles whose non-common sides form a right angle.

-Linear Pair is a pair of adjacent angles whose non-common sides form a line.

-Consecutive Angles are angles sharing a side, but having different vertices.

## Prove Linear Pair

Reasons Statements

Angle 1 and Angle 2 form a L.P. Given

Angle TAM is a straight angle Def. of L.P.

measure of angle TAM=180 degrees Def of straight /_

measure of angle TAM=180 degrees Def. of Straight /_

m. angle 1+m. angle 2=m. angle TAM Angle Add. Pos.

m. angle 1+m. angle 2=180 degrees Sub. Prop.=

Angle 1 and angle 2 are supp. Def. of Supp.

Angle 1 and Angle 2 form a L.P. Given

Angle TAM is a straight angle Def. of L.P.

measure of angle TAM=180 degrees Def of straight /_

measure of angle TAM=180 degrees Def. of Straight /_

m. angle 1+m. angle 2=m. angle TAM Angle Add. Pos.

m. angle 1+m. angle 2=180 degrees Sub. Prop.=

Angle 1 and angle 2 are supp. Def. of Supp.

## Prove Vertical Angles Theorem

Reasons Statements

angle 1 and angle 2 are VA Def. of VA

angle 1 and angle 3 form LP Def. of LP

angle 2 and angle 3 form LP

m. angle 1+m. angle 3=180 LP Theorem

m. angle 2+m. angle 3=180

m. angle 1=180-m. angle 3 Sub. Prop. =

m.angle 2=180-m. angle 3

angle 1 and angle 2 have equal measures Sub. Prop. =

angle 1 and angle 2 are VA Def. of VA

angle 1 and angle 3 form LP Def. of LP

angle 2 and angle 3 form LP

m. angle 1+m. angle 3=180 LP Theorem

m. angle 2+m. angle 3=180

m. angle 1=180-m. angle 3 Sub. Prop. =

m.angle 2=180-m. angle 3

angle 1 and angle 2 have equal measures Sub. Prop. =

Corresponding, Alternate Exterior, Alternate Interior, Sam Side Exterior, and Same Side Interior

## Parallel Lines(translations) and Perpendicular Lines(rotations)

Two lines are parallel if and only if one can be mapped onto the other with a translation(slide.)

Two lines are perpendicular if and only if one can be mapped onto the other with a 90 degree rotation.

Two lines are perpendicular if and only if one can be mapped onto the other with a 90 degree rotation.

## Corresponding Angles Postulate

If Corresponding Angles, formed by a transversal across 2 parallel lines, then angles are congruent.