Geometry Unit 3

Right Triangle

A triangle with one 90° angle.

Leg

Either of the two sides that form the right angle.

Hypotenuse

The side opposite the 90° angle; always the longest side.

Pythagorean Triple

Three whole numbers that satisfy $a^2 + b^2 = c^2$.

Congruent Right Triangles

Right triangles that are the same size and shape.

HL (Hypotenuse-Leg)

A right-triangle congruence shortcut using the hypotenuse and one leg.

LL (Leg-Leg)

A right-triangle congruence shortcut using both legs.

LA (Leg-Angle)

A right-triangle congruence shortcut using a leg and an acute angle.

HA (Hypotenuse-Angle)

A right-triangle congruence shortcut using the hypotenuse and an acute angle.

Angle Bisector

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

Perpendicular Bisector

A line that cuts a segment at its midpoint and at a 90° angle.

Similar Triangles

Triangles with the same shape; corresponding angles are congruent and sides are proportional.

AA Similarity

Two triangles are similar if two pairs of corresponding angles are congruent.

Altitude

A perpendicular segment from a vertex to the opposite side or its extension.

Hypotenuse Segments

The two parts of the hypotenuse created when an altitude is drawn to it.

Geometric Mean

The positive number $x$ such that $\frac{a}{x} = \frac{x}{b}$, so $x = \sqrt{ab}$.

45°-45°-90° Triangle

A right triangle with two 45° angles and congruent legs.

30°-60°-90° Triangle

A right triangle with angles of 30°, 60°, and 90°.

Special Right Triangle

A right triangle with predictable side-length relationships.

Right Triangle Altitude Theorem

Drawing an altitude to the hypotenuse creates two smaller triangles similar to the original triangle.