High School Geometry - Unit 1

Unit 1 of the High School Geometry Course

Point

A 0D location in space with no size, width, or depth.

Line

A 1D figure that is perfectly straight, has no thickness, and extends infinitely in both directions.

Plane

A 2D flat surface that has no thickness and extends infinitely in all directions.

Collinear

Points that lie on the same straight line.

Coplanar

Points or lines that lie on the same flat plane.

Line Segment

A straight path that is a measurable part of a line, bound by two specific endpoints.

Distance Formula

The formula used to find the length between two points $(x_1,y_1)$ and $(x_2,y_2)$: $d=\sqrt{(x_2-x_1)²+(y_2-y_1)²}$.

Midpoint

The exact middle point that divides a line segment into two equal halves.

Midpoint Formula

The coordinates used to find the center of a segment between $(x_1,y_1)$ and $(x_2,y_2)$: $M=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$.

Ray

A part of a line that starts at an endpoint and extends infinitely in one direction.

Angle

A figure formed by two rays sharing a common endpoint (called the vertex).

Interior

The region of space enclosed between the two rays of an angle.

Exterior

The region of space outside the rays of an angle.

Acute Angle

An angle that measures strictly between $0^\circ$ and $90^\circ$.

Obtuse Angle

An angle that measures strictly between $90^\circ$ and $180^\circ$.

Right Angle

An angle that measures exactly $90^\circ$.

Angle Bisector

A ray or line that divides an angle into two perfectly congruent (equal) adjacent angles.

Complementary Angles

Any two angles whose measures add up to exactly $90^\circ$.

Supplementary Angles

Any two angles whose measures add up to exactly $180^\circ$.

Adjacent Angles

Two angles that sit next to each other, sharing a common vertex and a common side, but no interior space.

Linear Pair

A pair of adjacent angles whose non-common sides form a straight line (they always add up to $180^\circ$).

Vertical Angles

A pair of non-adjacent, opposite angles formed by two intersecting lines (they are always equal/congruent).

Polygon

A closed, flat 2D shape made up of three or more straight line segments.

Triangle

A 3-sided polygon.

Quadrilateral

A 4-sided polygon.

Pentagon

A 5-sided polygon.

Hexagon

A 6-sided polygon.

Heptagon

A 7-sided polygon.

Octagon

A 8-sided polygon.

Nonagon

A 9-sided polygon.

Decagon

A 10-sided polygon.

Hendecagon

A 11-sided polygon.

Dodecagon

A 12-sided polygon.

$n$-gon

A polygon with $n$ number of sides (e.g., a 15-gon).

Convex Polygon

A polygon where no interior angle is greater than $180^\circ$ (no sides "cave in").

Concave Polygon

A polygon with at least one interior angle greater than $180^\circ$ (at least one vertex points inward like a “cave”).

Regular Polygon

A polygon that is both equilateral (all sides equal) and equiangular (all angles equal).

Perimeter

The total continuous distance around the outside edge of a 2D shape.

Perimeter of a Triangle

$P=a+b+c$ (the sum of all three sides).

Perimeter of a Square

$P = 4s$ (where $s$ is the side length).

Perimeter of a Rectangle

$P = 2l + 2w$ (where $l$ is length and $w$ is width).

Circumference

The total distance around the edge of a circle. Formula: $C = 2\pi r$ or $C = \pi d$.

Area

The total amount of 2D space enclosed inside a flat shape, measured in square units.

Area of a Triangle

$A = \dfrac{1}{2}bh$ (where $b$ is base and $h$ is height).

Area of a Square

$A = s^2$ (where $s$ is the side length).

Area of a Rectangle

$A = lw$ or $A = bh$ (length $\times$ width).

Area of a Circle

$A = \pi r^2$ (where $r$ is the radius).

Edge

The line segment where two flat faces of a 3D figure meet.

Vertex

The corner point where three or more edges of a 3D figure meet.

Face

A flat, 2D surface (usually a polygon) that forms the side of a 3D solid object.

Prism

A 3D solid with two identical, parallel polygon bases, and flat rectangular sides.

Pyramid

A 3D solid with one polygon base and triangular sides that meet at a single point (apex).

Surface Area

The total sum of the areas of all the outer faces and surfaces of a 3D object.

Volume

The total amount of 3D space enclosed inside a solid object, measured in cubic units.