Triangles and Congruence

These flashcards cover key vocabulary related to triangles, their classification, properties, and congruence according to the lecture notes.

Triangle

A closed figure in a plane consisting of three segments called sides.

Vertex

The point at which two sides of a triangle intersect.

Equilateral Triangle

A triangle with three congruent sides.

Isosceles Triangle

A triangle with at least two sides congruent.

Scalene Triangle

A triangle with no two sides congruent.

Acute Triangle

A triangle with three acute angles.

Obtuse Triangle

A triangle with one obtuse angle.

Right Triangle

A triangle with one right angle.

Hypotenuse

The side opposite the right angle in a right triangle.

Altitude

A segment drawn from a vertex perpendicular to the opposite side or extension of that side.

Median

A segment having one endpoint at a vertex of a triangle and the other endpoint at the midpoint of the opposite side.

Angle Bisector

The segment that bisects an angle of a triangle.

Point of Concurrency

The point where three or more lines intersect.

Congruent Triangles

Two triangles are congruent if their corresponding sides and angles are congruent.

SSS Congruence Postulate

Two triangles are congruent if three sides of one triangle are congruent to three sides of another triangle.

SAS Congruence Postulate

Two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

ASA Congruence Postulate

Two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle.

AAS Congruence Theorem

If two angles and a side (not included) of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent.

Leg-Leg Theorem

If two legs of one right triangle are congruent to two legs of a second right triangle, then the right triangles are congruent.

Triangle Inequality Theorem

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