Triangle and Geometric Theorems

Vocabulary flashcards reviewing essential triangle properties, inequalities, and geometric bisector theorems.

Isoceles triangle theorem

If the two legs are congruent, opposite base angles are too.

Equilateral triangle theorem

A theorem stating that the triangle has all equal sides and all equal angles; it is a type of isoceles triangle where all angles equal $60$.

Base angles theorem

If two legs are congruent, base angles are congruent.

Base angles theorem converse

Base angles are congruent, if two legs are congruent.

Triangle inequality theorem

To make a triangle, the addition of the smaller sides must be greater than the length of the longest side ($a + b > c$ or $c < a + b$).

Possible range of a third side

The inequality defining the third side length constraint: $a - b < c < a + b$.

Opposite side angle relationship

The opposite side of an angle is the smallest if that angle is the smallest.

Hinge theorem

If two triangles have two congruent pairs of sides, the triangle with the larger included angle has the longer third side.

Perpendicular bisector theorem

If a point lies on the perpendicular bisector of a line, it is equidistant from the endpoints of the segment.

Perpendicular bisector theorem converse

If a point is equidistant from the endpoints of a segment, the point is on the perpendicular bisector of the line segment.

Angle bisector theorem

If a point lies on the bisector of an angle, the point is equidistant from the sides of the angle.

Angle bisector theorem converse

If an interior point is equidistant from the sides of an angle, it is on a bisector.

Exterior angles theorem

Exterior angle equals the addition of remote interior angles.