Angle Sum Theorem, Triangle Properties, and Geometry Fundamentals

Vocabulary flashcards covering fundamental geometry concepts, angle pair relationships, triangle classifications, and geometric reasoning theorems.

Point

A location or position in geometry that has no size.

Line

A straight path that extends in two opposite directions without ending and contains an infinite amount of points.

Line Segment

A part of a line that consists of two endpoints and all points between them, containing an infinite amount of points.

Collinear Points

Points that lie on the same line.

Distance Between Two Points

The measure of a straight line segment connecting two points, expressed with segment additions such as $AB + BC + CD = AD$.

Plane

A flat surface that extends without end and contains infinitely many lines.

Coplanar

Points and/or lines that lie on the same plane.

Adjacent Angles

Two angles that have a common vertex and a common side, and are next to each other.

Vertical Angles

The pairs of nonadjacent angles formed by two intersecting lines.

Complementary Angles

Two angles whose measures have a sum of $90^\circ$, where each angle is called the complement of the other.

Supplementary Angles

Two angles whose measures have a sum of $180^\circ$, where each angle is called the supplement of the other.

Linear Pair

A pair of adjacent supplementary angles.

Angle Bisector

A line, line segment, or ray that divides an angle into two congruent angles.

Equilateral Triangle

A triangle in which all sides are congruent.

Isosceles Triangle

A triangle with two congruent sides.

Scalene Triangle

A triangle in which no sides are congruent.

Acute Triangle

A triangle in which all angles are acute.

Obtuse Triangle

A triangle containing one obtuse angle.

Right Triangle

A triangle containing one right angle ($90^\circ$).

Angle Addition Postulate

The principle stating that adjacent angle measures sum to the total angle measure, such as $m\angle QRT + m\angle SRT = m\angle QRS$.

Perpendicular Lines Property

Perpendicular ($\perp$) lines intersect to form right angles.

Triangle Angle Sum Theorem

The rule stating that the sum of the angle measures of a triangle is $180^\circ$ ($m\angle A + m\angle B + m\angle C = 180^\circ$).

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles ($m\angle 1 + m\angle 2 = m\angle 3$).

Isosceles Triangle Angle-Side Theorem

If two angles in a triangle are congruent ($\cong$), then the sides opposite those angles are congruent ($\cong$).

Linear Pair Theorem

The rule stating that linear pairs of angles are supplementary and sum to $180^\circ$.

Angles at a Point Theorem

The geometric rule stating that all angles surrounding a single point sum to $360^\circ$ ($m\angle 1 + m\angle 2 + m\angle 3 = 360^\circ$).

Vertical Angles Theorem

The theorem stating that vertical angles formed by intersecting lines are congruent ($\cong$).

Complementary Angle Sum Property

Two angles are complementary when their measures sum to $90^\circ$.