Geometry Theorems and Postulates and Definitions

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Reflexive Property

Any segment or angle is congruent to itself.

SSS (side-side-side)

If the 3 sides of a triangle are congruent to the corresponding sides of the other triangle, then the two triangles are congruent.

SAS (side-angle-side)

If 2 sides of one triangle and the included angle are congruent to the corresponding sides and angle of the other triangle then the two triangles are congruent.

ASA (angle-side-angle)

If 2 angles and the included side of one triangle are congruent to the corresponding side and angles of the other triangle, then the 2 triangles are congruent.

HL (hypotenuse-leg)

Two right triangles are congruent if the corresponding hypotenuses are congruent and 1 pair of corresponding legs are congruent.

Right ∠'s are ≅

If two angles are right angles then, they are congruent.

Straight ∠'s are ≅

If two angles are straight angles then they are congruent.

∠'s supp to the same ∠'s are ≅

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

∠'s supp to ≅ ∠'s are ≅

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

∠'s comp to the same ∠'s are ≅

If two angles are complementary to same angle, then they are congruent.

∠'s comp to ≅ ∠'s are ≅

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

Converse of a Conditional Statement

If Q, then P

Conditional Statement

If P, then Q

Inverse of a Conditional Statement

If not P, then not Q

Contrapositive of a Conditional Statement

If not Q, then not P

If a conditional statement is true, then the contrapositive is true as well.

If p, then q ↔ If ~p, then ~q

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