Triangle Theorems and Properties

Vocabulary flashcards covering key triangle theorems, relationships, and geometric definitions.

Triangle Sum Theorem

States that the sum of the three interior angles in a triangle is always $180^\circ$ ($\angle a + \angle b + \angle c = 180^\circ$).

Exterior Angle Theorem

States that the measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles ($\angle d = \angle a + \angle b$).

Midsegment

A segment in a triangle that is parallel to the triangle's base and one-half its length.

Pythagorean Inequality Theorem

A theorem used to classify triangles based on side lengths: right triangle ($c^2 = a^2 + b^2$), acute triangle ($c^2 < a^2 + b^2$), and obtuse triangle ($c^2 > a^2 + b^2$).

Triangle Inequality Theorem

States that the sum of any two sides of a triangle must be greater than the measure of the third side; used to determine if a triangle can exist given the lengths of three sides.

Angle Bisector Theorem

States that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Triangle Proportionality Theorem

States that if a line parallel to one side of a triangle intersects the other two sides, then it divides those two sides proportionally.