Special Triangles

Study Guide

Terms and Formulae

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Terms and Formulae

Terms

30-60-90 Triangle

A triangle with a 30, 60, and 90 degree angle.
45-45-90 Triangle

A triangle with a two 45 degree angles and one 90 degree angle.
Acute Triangle

A triangle with three acute angles.
Base Angle

An angle of an isosceles triangle opposite one of the equal sides, i.e. opposite one of the legs.
Base of an Isosceles Triangle

The side of an isosceles triangle unequal to the other two sides, the legs.
Equiangular Triangle

A triangle whose angles are all equal.
Equilateral Triangle

A triangle whose sides are all equal (of equal length).
Hypotenuse

The side of a right triangle opposite the right angle. The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the square of the other two sides.
Isosceles Triangle

A triangle with at least two equal sides.
Legs of a Right Triangle

The two sides of a right triangle opposite the two oblique angles.
Legs of an Isosceles Triangle

The two sides of an isosceles triangle that are equal.
Obtuse Triangle

A triangle with one obtuse angle.
Pythagorean Theorem

The theorem that states that the length of the hypotenuse squared is equal to the sum of the squares of the lengths of the legs of a right triangle; c² = a² + b².
Pythagorean Triple

A set of three integers a, b, and c such that c² = a² + b²
Right Triangle

A triangle with one right angle.
Scalene Triangle

A triangle with no equal sides.
Vertex Angle

The angle in an isosceles triangle opposite the base.

Formulae

Length of Hypotenuse

c =

a² + b²), where a and b are the lengths of the legs.

Length of a Leg

a =

c² - b²), where c is the length of the hypotenuse and b is the length of the other leg.

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