Angles

Acute Angle

An angle that measures less than 90 degrees but more than 0 degrees

Obtuse Angle

An angle whose measurement is between greater than 90 but less than 180 degrees

Angle

Angles are created by two distinct rays that share a common endpoint (also known as a vertex). ∠ABC or ∠B denote angles with vertex B.

Adjacent Angles

Angles in the same plane that have a common vertex and a common side, but no common interior points.

Segment Addition Postulate

Given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC

Congruent

Having the same size, shape and measure. Two figures are congruent if all of their corresponding measures are equal.

Angle Addition Postulate

If B is in the interior of angle AOC, then AOB + BOC = AOC. That is, the measure of the larger angle is the sum of the measures of the two smaller ones.

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary.

Converse of the Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite the angles are congruent.

Supplementary Angles

Two angles whose sum is 180 degrees.

Complementary Angles

Two angles whose sum is 90 degrees. Each angle is called the complement of the other.

Vertical Angles

Two nonadjacent angles formed by intersecting lines or segments. Also called opposite angles.

Bisector

A bisector divides a segment or angle into two equal parts.

Midpoint

A point on a segment that bisects the segment

Linear Pair

Adjacent, supplementary angles. Excluding their common side, a linear pair forms a straight line.

Straight Angle

An angle measuring exactly 180 degrees

Right Angle

An angle measuring exactly 90 degrees

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent.

Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Equiangular

The property of a polygon whose angles are all congruent.

Equilateral

The property of a polygon whose sides are all congruent.

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180°.

Vertical Angle Theorem

Vertical angles are congruent.

Exterior Angle of a Polygon

an angle that forms a linear pair with one of the angles of the polygon.

Remote Interior Angles of a Triangle

the two angles non-adjacent to the exterior angle.