Triangle Congruence & Geometry Flashcards

Flashcards covering triangle congruence and geometry theorems.

Given

Information directly stated in the problem.

Vertical Angles Are Congruent

Angles formed by intersecting lines are always equal.

Reflexive Property

A segment or angle is congruent to itself.

Definition of Midpoint

A midpoint splits a segment into two equal parts.

Definition of Angle Bisector

An angle bisector divides an angle into two congruent angles.

SSS (Side-Side-Side)

Three sides of one triangle are congruent to three sides of another.

SAS (Side-Angle-Side)

Two sides and the included angle are congruent.

ASA (Angle-Side-Angle)

Two angles and the included side are congruent.

AAS (Angle-Angle-Side)

Two angles and a non-included side are congruent.

HL (Hypotenuse-Leg)

For right triangles only: hypotenuse and one leg are congruent.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent. Use after proving triangles are congruent.

Definition of Congruent Segments

Segments that have the same length.

Definition of Congruent Angles

Angles that have the same measure.

Linear Pair Theorem

If two angles form a linear pair, they are supplementary (sum to 180 degrees). Use to find unknown angles.

Right Angles Are Congruent

All right angles measure 90 degrees, so they are congruent.

Definition of Perpendicular Lines

Two lines that intersect to form right angles. Use to prove right triangles or right angles.

Alternate Interior Angles Theorem

If lines are parallel, alternate interior angles are congruent.

Corresponding Angles Postulate

If lines are parallel, corresponding angles are congruent.

Third Angles Theorem

If two angles in one triangle are congruent to two in another, the third angles are also congruent. Used in ASA and AAS proofs.

Definition of Isosceles Triangle

A triangle with at least two congruent sides. The base angles are congruent too.

Definition of Equilateral Triangle

All sides are congruent and all angles measure 60 degrees. Use to justify side and angle congruence.