Geometry Foundations, Definitions, and Theorems

Comprehensive vocabulary flashcards covering geometric definitions, properties of equality, triangle congruence criteria, parallel line angle theorems and their converses, and polygon classifications.

Perpendicular

Two lines intersect to form a $90$ angle.

Bisector

A line/ray/segment that divides a segment/angle into $2 =$ pieces.

Midpoint

The middle point of a segment.

Adjacent

"Next to" each other

Linear Pair

$2$ angles that are adjacent and supplementary. (They form a straight line)

Complementary

$2$ angles that add to $90$ degrees.

Supplementary

$2$ angles that add to $180$ degrees.

Vertical Angles

Angles across from each other. Vertical angles are congruent.

Acute Angle

An angle $x$ so that $0 < x < 90$

Obtuse Angle

An angle $x$ so that $90 < x < 180$

Collinear

Points on the same line

Isosceles Triangle

A triangle with $2$ congruent sides

Equilateral Triangle

A triangle with $3$ congruent sides.

Parallelogram (Basic)

A quadrilateral with opposite sides parallel.

Rectangle

A quadrilateral with $4$ right angles

Square

A quadrilateral with $4$ right angles and $4$ congruent sides.

Rhombus

A quadrilateral with $4$ congruent sides

Quadrilateral

A polygon with $4$ sides.

Polygon

A closed shape made out of straight segments with no overlap.

Regular Polygon

A polygon with all equal angle and all equal sides.

Kite

A quadrilateral with $2$ sets of consecutive congruent sides.

Reflexive

A number, segment, or angle equal to itself.

Transitive

If $a = b$ and $b = c$, then the transitive property shortens this by saying $a = c$.

Substitution

To replace

Segment Addition Postulate

Two smaller segments equals a bigger segment.

Angle Addition Postulate

Two smaller angles equals a bigger angle.

APOE

Addition property of equality = "Add on both sides"

SPOE

Subtraction property of equality = "subtract on both sides"

DPOE

Division property of Equality = "divide on both sides"

MPOE

Multiplication property of equality = "multiply on both sides"

Property of Equality

"to both sides"

Degree of a Circle

is $360$ degrees

Pythagorean Theorem

If given a right triangle, then $a^2 + b^2 = c^2$

Hypotenuse Leg Theorem

In a pair of right triangles, if a pair of legs and hypotenuses are marked congruent, then the triangles are congruent.

Def. of a Circle

The set of all points equidistant to $1$ point.

Def. of Perp. Bisector

The set of all points equidistant to $2$ points.

Equidistant

Equal distance

Consecutive

"one right after the other"

SAS

In $2$ triangles, if $2$ pairs of sides and their included angle are congruent, then the triangles are congruent.

ASA

In $2$ triangles, if $2$ pairs of angles and their included sides are congruent, then the triangles are congruent.

SSS

In $2$ triangles, if $3$ pairs of sides are congruent, then the triangles are congruent.

AAS

In $2$ triangles, if $2$ pairs of angles and a non-included sides are congruent, then the triangles are congruent.

Def. of Congruent

equal pieces.

Def. of Congruent Figures

If $2$ figures are congruent, then so are each of their corresponding parts.

Triangle Sum Theorem

In interior angles in a triangle add to $180$.

Alt. Interior Angles Theorem

If lines are parallel, then alternate interior angles are congruent.

Alt. Interior Angles Theorem Converse

If alternate interior angles are congruent, then lines are parallel.

Alt. Exterior Angles Theorem

If lines are parallel, then alternate exterior angles are congruent.

Alt. Ext. angles Theorem Converse

If alternate exterior angles are congruent, then lines are parallel.

Corresponding Angles Theorem

If lines are parallel, then corresponding angles are congruent.

Corresponding angles Theorem Converse

If corresponding angles are congruent, then lines are parallel.

Consecutive Angles Theorem

If lines are parallel, then consecutive interior angles are supplementary.

Consecutive Angles Theorem Converse

If consecutive interior angles are supplementary, then lines are parallel.

When does ASS happen?

When you have an angle that is NOT between the two given congruent sides in a triangle.

Auxiliary Lines

A line drawn to add support to a proof. (example, diagonals, perpendicular. bisectors, angle bisector. These are not random lines, they are purposeful.)

Third Angles Theorem

If $2$ pairs of angles are congruent between $2$ triangles, THEN THE THIRD PAIR must be congruent.