Geometric Proofs of Congruence and Similarity

This set of vocabulary flashcards covers the fundamental definitions and geometric proofs for triangle congruence and similarity, as well as the defining properties of various quadrilaterals.

Congruent

A term describing two shapes that are exactly the same.

Similar

A term describing two shapes where one is an enlarged or shrunken version of another.

Side-Side-Side (SSS) Congruence

Two triangles are congruent ($\cong$) if all three sides of one triangle are equal to the corresponding three sides of another triangle.

Side-Angle-Side (SAS) Congruence

Two triangles are congruent ($\cong$) if two sides of one triangle are equal in length to two sides of another triangle, and the angle between those two sides is the same in both triangles.

Angle-Side-Angle (ASA) Congruence

Two triangles are congruent ($\cong$) if two angles of one triangle are equal to two angles of another triangle, and the side between those two angles is the same length in both triangles.

Angle-Angle-Side (AAS) Congruence

Two triangles are congruent ($\cong$) if two angles of one triangle are equal to two angles of another triangle, and a non-included side (a side not between the two angles) is the same length in both triangles.

Hypotenuse

The side opposite the right angle in a right-angled triangle.

Right Angle-Hypotenuse-Corresponding Side (RHS) Congruence

Two right-angled triangles are congruent ($\cong$) if the hypotenuse of one triangle is equal to the hypotenuse of the other triangle, and one corresponding leg (side adjacent to the right angle) is equal in both triangles.

Side-Side-Side (SSS) Similarity

Two triangles are similar ($\sim$) if all sides of the one triangle are all either enlarged or shrunk by the same factor to produce the second triangle.

Side-Angle-Side (SAS) Similarity

Two triangles are similar ($\sim$) if there is one matching angle in each and they are formed by a pair of sides that are in ratio with the matching pair in the other triangle.

Angle-Angle (AA) Similarity

Two triangles are similar ($\sim$) if there are two pairs of matching angles.

Square

A quadrilateral with four equal sides, opposite sides parallel, all angles equal to $90^\circ$, and diagonals that bisect each other, are the same length, and meet at $90^\circ$.

Rectangle

A quadrilateral with two pairs of equal sides, opposite sides parallel, all angles equal to $90^\circ$, and diagonals that bisect each other and are of the same length.

Parallelogram

A quadrilateral with two pairs of equal sides, opposite sides parallel, two diagonally opposite equal angles (summing to $360^\circ$), and diagonals that bisect each other.

Rhombus

A quadrilateral with four equal sides, opposite sides parallel, two diagonally opposite equal angles (summing to $360^\circ$), and diagonals that bisect each other and meet at $90^\circ$.

Trapezium

A quadrilateral with one pair of parallel sides, no diagonal properties, and angles that sum to $360^\circ$.