Geometry Proofs

Radii in a circle are congruent

The radii of the same circle or of congruent circles are equal in length.

Transitive Property

If one quantity equals a second, and the second equals a third, then the first equals the third.

Addition Property

If equal quantities are added to equal quantities, the sums are equal.

Subtraction Property

If equal quantities are subtracted from equal quantities, the differences are equal.

Reflexive Property

Any quantity is equal to itself.

Perpendicular lines form right angles

When two lines intersect to form right angles, they are perpendicular.

All right angles are congruent

Any two right angles have the same measure (90°), so they are congruent.

All straight angles are congruent

Any two straight angles (180°) are congruent because they have equal measure.

Supplements of congruent angles are congruent

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

Supplements of the same angle are congruent

If two angles are supplementary to the same angle, they are congruent to each other.

Complements of congruent angles are congruent

If two angles are each complementary to congruent angles, they are congruent.

Complements of the same angle are congruent

If two angles are complementary to the same angle, they are congruent to each other.

Vertical angles are congruent

When two lines intersect, the opposite (vertical) angles formed are equal in measure.

Definition of segment bisector

A line, ray, or segment that passes through the midpoint of a segment, dividing it into two congruent parts.

Definition of angle bisector

A ray that divides an angle into two congruent angles.

Definition of midpoint

The point that divides a segment into two congruent parts.

Halves of equals are equal

If two quantities are equal, then their halves are also equal.

SAS (Side-Angle-Side)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

ASA (Angle-Side-Angle)

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent.

SSS (Side-Side-Side)

If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.