Unit 4: Congruent Triangles - ASA, AAS, and HL

Vocabulary flashcards covering triangle congruence theorems (ASA, AAS, HL) and key proof justifications including bisectors, midpoints, reflexive property, and angle relationships.

Hypotenuse-Leg (HL) Theorem

A theorem stating that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Hypotenuse

The side in a right triangle that is opposite the right angle.

Leg (of a Right Triangle)

A side in a right triangle that is adjacent to the right angle.

Angle-Angle-Side (AAS) Theorem

A theorem stating that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.

Non-Included Side

A side of a triangle that is located opposite the specified angles rather than situated between them.

Angle-Side-Angle (ASA) Theorem

A congruence theorem used to prove two triangles are congruent when two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

Reflexive Property of Congruence

A geometric property asserting that a shared geometric segment or angle is congruent to itself (for example, $\overline{BD} \cong \overline{BD}$ or $\overline{MP} \cong \overline{MP}$).

Definition of an Angle Bisector

A geometric definition stating that a ray or segment divides an angle into two congruent angles (for example, if $\overline{BD}$ bisects $\angle ABC$, then $\angle ABD \cong \angle DBC$).

Definition of a Midpoint

A geometric definition stating that a point divides a segment into two congruent segments (for example, if $C$ is the midpoint of $\overline{AD}$, then $\overline{AC} \cong \overline{CD}$).

Vertical Angles

Opposite angles formed by the intersection of two lines, which are always congruent (for example, $\angle QRP \cong \angle SRT$).

Alternate Interior Angles

Pairs of non-adjacent interior angles lying on opposite sides of a transversal crossing two parallel lines, which are congruent (for example, used when $\overline{ST} \parallel \overline{UV}$).

Corresponding Angles

Pairs of angles lying in the same relative position at each intersection where a transversal crosses two parallel lines, which are congruent (for example, used when $\overline{AB} \parallel \overline{CE}$).