Triangles, Special Line Segments, and Corollaries

A set of vocabulary flashcards defining different classifications of triangles, parts of isosceles and right triangles, special interior line segments, and key corollaries to the Side-Angle Theorem.

Scalene triangle

A triangle in which no two sides are congruent.

Isosceles triangle

A triangle in which at least two sides are congruent.

Equilateral triangle

A triangle in which all sides are congruent.

Equiangular triangle

A triangle in which all angles are congruent.

Right triangle

A triangle in which one of the angles is a right angle.

Acute triangle

A triangle in which all angles are acute.

Obtuse triangle

A triangle in which one of the angles is obtuse.

Legs (of an isosceles triangle)

The two congruent sides of an isosceles triangle.

Base (of an isosceles triangle)

The third side of an isosceles triangle.

Base angles (of an isosceles triangle)

The two angles whose common side is the base.

Vertex angle (of an isosceles triangle)

The third angle formed by the congruent sides of an isosceles triangle.

Legs (of a right triangle)

The two sides that form the right angle.

Hypotenuse

The third side of a right triangle.

Cevian

A line segment drawn from a vertex of a triangle to a point on the opposite side.

Median (of a triangle)

A line segment that joins any vertex of a triangle to the midpoint of the opposite side.

Altitude (of a triangle)

A line segment drawn from any vertex of a triangle perpendicular to, and ending on, the opposite side or an extension of the opposite side.

Angle bisector (of a triangle)

A line segment which bisects any angle of the triangle and terminates on the side opposite the angle.

Vertex Angle Bisector Corollary (Side-Angle Theorem)

If a line segment bisects the vertex angle of an isosceles triangle, then it is also the altitude and median to the base.

Altitude to the Base Corollary (Side-Angle Theorem)

If a line segment is the altitude to the base of an isosceles triangle, then it is also the median to the base and the bisector of the vertex angle.

Median to the Base Corollary (Side-Angle Theorem)

If a line segment is the median to the base of an isosceles triangle, then it is also the altitude to the base and the bisector of the vertex angle.

Equilateral-Equiangular Corollary

If a triangle is equilateral, then it is equiangular.

Equiangular-Equilateral Corollary (Converse)

If a triangle is equiangular, then it is equilateral.