Geometry Theorems

Theorem 4 Congruent Supplements Theorem

If angles are supplementary to the same angle, then they are congruent

Theorem 5 Congruent Supplements Theorem

If angles are supplementary to congruent angles, then they are congruent.

Theorem 6 Congruent Complements Theorem

If angles are complementary to the same angle, then they are congruent

Theorem 7 Congruent Complements Theorem

If angles are complementary to congruent angles, then they are congruent

Definition 2.2: supplementary

If two angles are supplementary, then they form a straight angle

If two angles form a straight angle, then they are supplementary

Definition 2.2: complementary

If two angles are complementary, then they form a right angle

If two angles form a right angle, then they are complementary.

Definition 2.2: perpendicular

If 2 lines are perpendicular then they form a right angle

If an angle is right then the 2 lines are perpendicular

Theorem 2.2: ray/right angle

If a ray divides an angle into two complementary angles then the original angle is a right angle

Definition2.2: intersect/perpendicular

If two lines intersect to form a right angle, the two lines are perpendicular

If two lines are perpendicular then they intersect to form a right angle

Theorem 8

If a segment is added to two congruent segments, then the sums are congruent

Theorem 9

If an angle is added to two congruent angles, then the sums are congruent.

Theorem 10

If congruent segments are added to congruent segments, then the sums are congruent

Theorem 11

If congruent angles are added to congruent angles, then the sums are congruent.

Theorem 12

If a segment (or angle) is subtracted from congruent segments (or angles), then the differences are congruent.

Theorem 13

If congruent segments (or angles) are subtracted from congruent segments (or angles), then the differences are congruent.

Theorem 14

If segments (or angles) are congruent, their like multiples are congruent. (Multiplication Property)

Theorem 15

If segments (or angles) are congruent, their like divisions are congruent. (Division Property)

Transitive Property

If a congruent to b and b congruent to c, then a congruent to c.

Theorem 16

If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other. (Transitive Property)

Theorem 17

If angles (or segments) are congruent to congruent angles (or segments), they are congruent to each other. (Transitive Property)

Theorem 18

Vertical angles are congruent.

Reflexive Property

A line or angle is congruent to itself.

Theorem 19

All radii of a circle are congruent

Isosceles Triangle Theorem

If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent.

If 2 angles of a triangle are congruent, then the sides opposite those sides are congruent.

Definition: Right angles/90 degrees

If an angle is 90 degrees then it is a right angle

If an angle is a righty angle then it is 90 degrees

Definition: Straight angles/180 degrees

If an angle is 180 degrees then it is a straight angle

If an angle is a straight angle then it is 90 degrees

Definition: Congruent angles

If angles (or segments) are equal, then they are congruent

If angles (or segments) are congruent, then they are equal

1.4 Theorem 1: Right angles/congruent

If two angles are right angles, then they are congruent

1.4 Theorem 2: Straight angles/congruent

If two angles are straight angles, then they are congruent

1.5 Theorem: Ray/congruent

If a ray bisects an angle, it divides the angle into 2 congruent angles

1.5 Theorem: line/congruent

If a line bisects an angle, it divides the segment into 2 congruent segments

1.5 Theorem: point/midpoint

If a point divides a segment into 2 congruent segments, it is the midpoint of the segment