PSAT 8/9 Math Geometry: Core Skills for Shapes, Space, and Reasoning

Line

Extends forever in two directions.

Line Segment

Has two endpoints.

Ray

Has one endpoint and extends forever in one direction.

Angle

Formed by two rays with a common endpoint.

Acute Angle

Measures less than $90^\text{°}$.

Right Angle

Measures exactly $90^\text{°}$.

Obtuse Angle

Measures between $90^\text{°}$ and $180^\text{°}$.

Straight Angle

Measures $180^\text{°}$.

Complementary Angles

Two angles whose measures add to $90^\text{°}$.

Supplementary Angles

Two angles whose measures add to $180^\text{°}$.

Vertical Angles

Opposite angles at an intersection that are always equal.

Linear Pair

Adjacent angles whose non-common sides form a straight line.

Transversal

A line that crosses two other lines.

Corresponding Angles

Angles that are equal when a transversal cuts parallel lines.

Alternate Interior Angles

Angles that are equal when a transversal cuts parallel lines.

Alternate Exterior Angles

Angles that are equal when a transversal cuts parallel lines.

Same-Side Interior Angles

Angles that are supplementary when a transversal cuts parallel lines.

Triangle

A polygon with three sides.

Sum of Interior Angles in a Triangle

Always equals $180^\text{°}$.

Exterior Angle of a Triangle

Equals the sum of the two remote interior angles.

Triangle Inequality Theorem

The sum of the lengths of any two sides must be greater than the length of the third side.

Isosceles Triangle

At least two equal sides, with equal angles opposite those sides.

Equilateral Triangle

All sides equal, with each angle measuring $60^\text{°}$.

Scalene Triangle

No equal sides.

Right Triangle

A triangle with one right angle ($90^\text{°}$).

Pythagorean Theorem

In a right triangle, $a^2 + b^2 = c^2$.

Area of Rectangle

$A = lw$, where $l$ is length and $w$ is width.

Area of Triangle

$A = \frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Volume of Rectangular Prism

$V = lwh$, where $l$ is length, $w$ is width, and $h$ is height.

Surface Area of Rectangular Prism

$SA = 2(lw + lh + wh)$.

Circumference of Circle

$C = 2\text{π}r$.

Area of Circle

$A = \text{π}r^2$.