Geometry Lecture: Angles, Triangles, and Polygons

Vocabulary practice covering angle pairs, triangle theorems, polygon interior angles, and properties of quadrilaterals.

Corresponding angles

Congruent angles in corresponding positions on the transversal.

Alternate interior angles

Congruent angles that lie between the two lines and on opposite sides of the transversal.

Alternate exterior angles

Congruent angles that lie outside the two lines and on opposite sides of the transversal.

Consecutive interior angles

Supplementary angles that lie between the two lines and on the same side of the transversal.

Linear Pair

Angles on the same line separated by a transversal that sum to $180^\circ$.

Midsegment

A segment that connects the midpoints of two sides of a triangle and is half as long as the base.

Longer Side Theorem

States that the angle opposite to the longer side is larger than the angle opposite the shortest side.

Larger Angle Theorem

States that the side opposite to the larger angle is larger than the side opposite the shortest angle.

Triangle Inequality

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

Interior Angles Formula ($S_n$)

The sum of the interior angles of a polygon with $n$ sides is $180(n-2)$.

Parallelogram

Opposite sides and angles are congruent, consecutive angles are supplementary, and diagonals bisect each other.

Rhombus

Four congruent sides, perpendicular diagonals, and diagonals that bisect pairs of opposite angles.

Rectangle

Four right angles and congruent diagonals.

Square

Four congruent sides and four right angles.