Triangle Congruence & Relationships

These flashcards cover definitions related to triangle congruence and relationships, including types of triangles, theorems, and properties.

Congruent Triangles

Triangles that have the same size and shape.

Congruence Transformation

A transformation that preserves length and angle measures, resulting in congruent figures.

Congruency Statement

A statement that indicates two triangles are congruent, often written in the form of a correspondence between their vertices.

Third Angle Theorem

If two angles of one triangle are equal to two angles of another triangle, then the third angles are also equal.

Acute Triangle

A triangle that has all angles less than 90 degrees.

Obtuse Triangle

A triangle that has one angle greater than 90 degrees.

Scalene Triangle

A triangle that has all sides of different lengths.

Equilateral Triangle

A triangle that has all sides of equal length.

Equiangular Triangle

A triangle that has all angles of equal measure.

Right Triangle

A triangle that has one angle equal to 90 degrees.

Isosceles Triangle

A triangle that has at least two sides of equal length.

Legs of an Isosceles Triangle

The two sides of an isosceles triangle that are of equal length.

Base of an Isosceles Triangle

The side of an isosceles triangle that is not one of the equal sides.

Base Angles of an Isosceles Triangle

The angles opposite the two equal sides in an isosceles triangle.

Vertex Angle of an Isosceles Triangle

The angle formed by the two legs of an isosceles triangle.

Isosceles Triangle Theorem

If two sides of a triangle are equal, then the angles opposite those sides are equal.

Converse of the Isosceles Triangle Theorem

If two angles of a triangle are equal, then the sides opposite those angles are equal.

SSS

Side-Side-Side: A criterion for triangle congruence stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

SAS

Side-Angle-Side: A criterion for triangle congruence stating that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, they are congruent.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent; used to justify that corresponding parts of congruent triangles are equal.

ASA

Angle-Side-Angle: A criterion for triangle congruence stating that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, they are congruent.

Included Side

The side between two angles in a triangle.

AAS

Angle-Angle-Side: A criterion for triangle congruence stating that if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, they are congruent.

Included Angle

The angle between two sides in a triangle.

Hypotenuse

The longest side of a right triangle, opposite the right angle.

Legs of a Right Triangle

The two sides of a right triangle that form the right angle.

HL

Hypotenuse-Leg: A criterion for triangle congruence applicable to right triangles.

Pythagorean Theorem

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Converse of the Pythagorean Theorem

States that if in a triangle, the square of the longest side is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Angle Bisector of a Triangle

A segment that bisects an angle of the triangle and extends to the opposite side.

Perpendicular Bisector of a Triangle

A line that divides a side of a triangle into two equal parts at a right angle.

Altitude

A segment from a vertex of a triangle perpendicular to the line containing the opposite side.

Median

A segment from a vertex of a triangle to the midpoint of the opposite side.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle and the included angle of the first triangle is larger than the included angle of the second triangle, then the length of the third side of the first triangle is greater than the length of the third side of the second triangle.