Geometry Terms and Definitions

Overlapping Figures

• Figures that are completely separate from each other.

• Figures which have interior points in common. They share at least one angle or side.

• Figures that are identical in shape and size.

• Figures that can be rotated but do not share any points.

Sufficient Condition

• A condition that is necessary but not sufficient for a conclusion.

• A condition that is enough to determine whether a figure is congruent.

• A condition that can be ignored in determining congruence.

• A condition that applies only to triangles.

SSS Theorem for Similar Triangles

• If two corresponding sides are proportional and the included angle is congruent, then the triangles are similar.

• If two triangles have equal angles, then their sides are proportional.

• If two triangles have equal sides, then their angles are congruent.

• If two corresponding sides are equal, then the triangles are congruent.

ASA Theorem for Congruent Triangles

• If two angles and the included side connecting them in one triangle are congruent to the corresponding angles and the included side of another triangle, then the triangles are congruent.

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

• If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar but not necessarily congruent.

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

Hypotenuse

• The longest side of a right triangle, the side opposite the right angle.

• The shortest side of a right triangle, adjacent to the right angle.

• The side opposite the largest angle in any triangle.

• The side that forms the right angle in a right triangle.

SAS Theorem for Congruent Triangles

• If two sides and the included angle connecting them are congruent, then the triangles themselves are also congruent.

• If two angles and the included side connecting them are congruent, then the triangles themselves are also congruent.

• If three sides of one triangle are equal to three sides of another triangle, then the triangles themselves are also congruent.

• If two sides are equal and the opposite angles are equal, then the triangles themselves are also congruent.

AA Theorem for Similar Triangles

• If two corresponding angles are congruent, then the triangles are similar.

• If two sides are proportional, then the triangles are similar.

• If the sum of the angles in one triangle is equal to the sum of the angles in another triangle, then the triangles are similar.

• If two angles are equal, then the triangles are congruent.

Nonoverlapping Figures

• Figures that share some interior points.

• Figures or regions that do not share any interior points. No sides or angles in common.

• Figures that are identical in shape and size.

• Figures that overlap partially.

Similar Figures

• Figures that have the same shape but not necessarily the same size.

• Figures that are identical in both shape and size.

• Figures that have different shapes but the same size.

• Figures that can be transformed into one another through rotation.

3rd Angle Theorem for Similar Triangles

• If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also be congruent.

• If two angles in one triangle are not congruent to two angles in another triangle, then the triangles are not similar.

• If two angles in one triangle are congruent to one angle in another triangle, then the triangles are similar.

• If all three angles in one triangle are equal to all three angles in another triangle, then the triangles are congruent.