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.
