Geometry: Congruence Theorems and Congruent Figures

Comprehensive vocabulary flashcards covering congruent figures, transformations, triangle congruence theorems (SSS, SAS, ASA, AAS, HL), CPCFC, and related geometric definitions.

Congruent Figures (Rigid Motion Definition)

Two figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions, such as translations, rotations, and reflections.

Rigid Motions

Transformations—specifically translations, rotations, and reflections—that move a figure without altering its size or shape.

Corresponding Parts

Pairs of sides and angles that are located in the same relative positions across polygons with an equal number of sides.

Congruence Statement

A formal statement that writes two geometric figures as congruent by matching corresponding vertices in the exact same order (for example, $\Delta ABC \cong \Delta DEF$).

Corresponding Parts of Congruent Figures are Congruent (CPCFC)

Two figures are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Third Angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are also congruent (even if not explicitly marked).

Included Side

In a triangle, the side connecting the vertices of two consecutive angles (the side located directly between two angles).

Angle-Side-Angle (ASA) Triangle Congruence Theorem

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

Included Angle

The angle formed by two consecutive sides of a triangle (the angle situated between the two sides).

Side-Angle-Side (SAS) Triangle Congruence Theorem

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

Side-Side-Side (SSS) Triangle Congruence Theorem

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

Non-Included Side

A triangle side that is not located between two reference angles.

Angle-Angle-Side (AAS) Triangle Congruence Theorem

If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.

Hypotenuse-Leg (HL) Triangle Congruence Theorem

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the right triangles are congruent.

Reflexive Property of Congruence

A geometric property stating that a geometric entity is congruent to itself (such as a shared side $\overline{QS} \cong \overline{QS}$ or a shared segment $\overline{NL} \cong \overline{NL}$).

Angle Bisector

A ray or segment that divides an angle into two congruent angles.

Segment Bisector

A line, segment, or ray that divides a line segment into two congruent segments at its midpoint.

Midpoint

A point on a line segment that divides it into two congruent parts (for example, point $C$ is the midpoint of $\overline{AF}$ if $\overline{AC} \cong \overline{CF}$).

Alternate Interior Angles

Pairs of interior angles on opposite sides of a transversal intersecting two parallel lines, which are congruent when the lines are parallel.

Vertical Angles

Opposite angles formed by the intersection of two lines, which are always congruent.