Unit 5 Review on Congruent Triangles

These flashcards cover key vocabulary and concepts related to congruent triangles, their properties, and techniques for proving their congruence.

Congruent Triangles

Triangles that are identical in size and shape, with corresponding sides and angles equal.

SSS Postulate

Side-Side-Side: If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

SAS Postulate

Side-Angle-Side: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

ASA Postulate

Angle-Side-Angle: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.

AAS Postulate

Angle-Angle-Side: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.

HL Theorem

Hypotenuse-Leg: In right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, the triangles are congruent.

Reflexive Property

A property that states that a quantity is equal to itself, often used in proofs of congruence.

Vertical Angles

Angles that are opposite each other when two lines intersect; vertical angles are always congruent.

Angle Bisector

A line that divides an angle into two equal parts, which can imply angles are congruent.

Midpoint

A point that divides a segment into two equal lengths.

Congruency Statement

A statement that indicates the congruence of two triangles, often using corresponding vertices.

Proving Congruence

The process of showing that two triangles are congruent through the application of postulates or theorems.

Marking Congruent Parts

The process of indicating which sides and angles of triangles are congruent in a diagram.

Distance Formula

A formula used to determine the distance between two points in the coordinate plane: d = √((x2-x1)² + (y2-y1)²).

Coordinates of Points

Specific values that define the position of points in the coordinate plane, often used to establish triangle congruence.

Proofs in Geometry

Logical arguments used to demonstrate the validity of statements in geometry, based on axioms and previously established results.

Congruent Sides

Sides of two triangles that are equal in length.

Congruent Angles

Angles of two triangles that are equal in measure.