All Geometry Terms, Properties, Formulas, Theorem, and Postulates

a composite list of everything i learned in geometry

Point

A point is a position in space. A point cannot move

Line

A line is a straight, continuous arrangement of infinite points

Collinear

Collinear means points that are lying on the same line

Noncollinear

Noncollinear means points that do not lie on the same line

Plane

A plane is a flat surface with infinite length and width

Ray

A ray is part of a line that begins at a point and extends forever

Opposite Ray

An opposite ray are two rays with the same endpoint that extend in opposite directions

Line Segment

A line segment is part of a line that includes two points and all collinear points between them

Coplanar

Coplanar are lines that are contained in the same plane

Noncoplanar

Noncoplanar are lines that are not contained in the same plane

Parallel Lines

Parallel Lines are lines with the same slope that run alongside each other that never intersect

Perpendicular Lines

Perpendicular Lines are lines that intersect at a 90° angle

Skew Lines

Skew Lines are lines that aren’t in the same plane, nor are they parallel or intersecting

Straightedge

A straightedge is any tool that has a straightedge

Compass

A compass is a tool used for drawing arcs and circles, as well as creating congruent lines and bisectors

Protractor

A protractor is a tool used to measure angles

Segment Addition Postulate

If B is between points A and C, then AB + BC = AC

Coordinate Plane

A coordinate plane is a two-dimensional plane formed by the intersection of two number lines, one going horizontal (x-axis) and the other going vertical (y-axis)

Midpoint

A midpoint is a point directly in the middle of a line segment

Midpoint Formula

(xₘ, yₘ) = (x₁ + x₂)/2, (y₁ + y ₂)/2

Angle

An angle is formed by two rays or line segments that share a common endpoint

Acute Angle

An acute angle is an angle less than 90°

Right Angle

An right angle is an angle measuring to 90°

Obtuse Angle

An obtuse angle is an angle less than 180° but more than 90°

Straight Angle

A straight angle is an angle measuring to 180°

Angle Addition Postulate

If line segment AD is in the interior of angle BAC, then the measurement of angle BAD + the measurement of angle DAC = the measurement of angle BAC

Adjacent Angles

Adjacent angles are two angles that share a common side and vertex, but share no interior poitns

Vertical Angles

Vertical angles are two congruent angles that have sides that form opposite rays; they are directly across from each other.

Linear Pair

A linear pair is two adjacent angles in which their noncommon sides are opposite rays; linear pairs form an angle that measures 180°

Complementary Angles

Complementary Angles are two angles whose measures add up to 90°. Each angle is called the complement of the other

Supplementary Angles

Supplementary Angles are two angles whose measures add up to 180°. Each angle is called the supplement of the other.

Angle Bisector

An Angle Bisector is a ray or line segment that splits an angle into two congruent parts.

Postulate

A postulate is a statement that are accepted as true

Congruence

Congruence means to be equal

Similarity

Similarity means same shape, different size

Theorem

A Theorem is a statement that can be proved using logic

Addition Property

If a=b, then a+b = b+c.

Subtraction Property

If a=b, then a-c = b -c.

Multiplication Property

If a=b, then a*c = b*c

Division Property

If a=b, and c ≠ 0, then, a/c = b/c

Reflexive Property

a=a

Symmetric Property

If a=b, then b=a

Transitive Property

If a=b, and b=c, then a=c

Substitution Property

If a=b, then b can replace a in any expression

Equal Complements Theorem

Complements of the same angle are equal in measure. If the measurement of angle 1 + the measurement of angle 2 = 90°, and the measurement of angle 2 + the measurement of angle = 90°, then the measurement of angle 1 is equal to the measurement of angle 3.

Equal Supplements Theorem

Supplements of the same angle are equal in measure. If the measurement of angle 1 + the measurement of angle 2 = 180°, and the measurement of angle 2 + the measurement of angle = 180°, then the measurement of angle 1 is equal to the measurement of angle 3.

Linear Pair Theorem

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

Vertical Angles Theorem

Vertical angles are congruent

Right Angles Theorem

Right angles are congruent and measure 90°

Equal Supplementary Angles Theorem

Two equal supplementary angles are right angles

Exterior

The exterior is the outside of two parallel lines

Interior

The interior is the inside of two parallel lines

Transversal

A transversal is when two parallel lines get intersected by a third line

Alternate Interior Angles

Alternate Interior Angles are two congruent angles in the interior of two parallel lines and on opposite sides of the transversal

Alternate Exterior Angles

Alternate Exterior Angles are two congruent angles in the exterior of two parallel lines and on opposite sides of the transversal

Corresponding Angles

Corresponding Angles are two congruent angles, one in the interior and one in the exterior, that are on the same side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are two angles in the exterior on the same side of the transversal; they always add up to 180°, additionally they are supplementary

Consecutive Interior Angles

Consecutive Interior Angles are two angles in the interior on the same side of the transversal; they always add up to 180°, additionally they are supplementary

Distributive Property

a(b+c) = ab + ac

Proof

Proof is a logical, step-by-step argument that uses established facts to prove a geometric statement is true

Triangle

A triangle is formed by three noncollinear points connected by segments

Vertex of a triangle

The vertex of a triangle is the point at which each of the segments connect

Sides

Sides are the segments of a shape

Included Side

The Included Side is the side between two given points

Reference Angle

The reference angle is the angle being referred to

Adjacent Sides

Adjacent Sides are the sides of which the reference angle is next to

Opposite Side

The Opposite Side is the side across from the included side

Included Angle

The Included Angle is the angle formed by two adjacent sides of a shape at their common vertex.

Acute Triangle

An Acute Triangle has only acute angles

Obtuse Triangle

An Obtuse Triangle one obtuse angle in the triangle

Equiangular Triangle

An Equiangular Triangle has only congruent angles

Right Triangle

A Right Triangle has one right angle

Isosceles Triangle

An Isosceles Triangle has two congruent sides

Scalene Triangle

A scalene triangle has no congruent sides

Equilateral Triangle

An equilateral triangle has only congruent sides

Legs of an Isosceles Triangle

The legs of an isosceles triangle are the two sides that are congruent

Base Angles

Base Angles are the angles across from the legs, they are also congruent

Vertex of an Isosceles Triangle

The vertex of an isosceles triangle is the angle formed by the legs

Base

The base is the side across from the vertex angle.

Triangle Sum Theorem

The Triangle Sum Theorem states that all three angles in a triangle will add up to 180°

Isosceles Triangle Theorem

The Isosceles Triangle Theorem states that in an isosceles triangle, the angles opposite from the equal sides are equal

Converse of Isosceles Triangle Theorem

The converse of the isosceles triangle theorem states if two angles in a triangle are congruent, the sides opposite from those angles are also congruent.

Remote Interior Angles

Remote Interior Angles are the two angles that are non-adjacent to the specified exterior angle

Exterior Angle Theorem

The measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle

Exterior Angle Inequality Theorem

The Exterior Angle Inequality Theorem states the measure of an exterior angle of a triangle is greater than the measure of either of the remote interior angles

Triangle Inequality Theorem

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