Geometry Formulas

For SAT prep.

What is the rule for 45-45-90 right triangles?

The legs are x, and the hypotenuse is x√2.

What is the rule for 60-30-90 triangles?

The short leg is x, the long leg is x√3, and the hypotenuse is 2x.

What are Pythagorean triples?

Sets of three positive integers (a, b, c) where a² + b² = c². The most common example is (3, 4, 5). Other examples include (5, 12, 13) and (8, 15, 17).

How do you find the area for a triangle?

The formula is 1/2bh.

What is the biggest, smallest, medium rule of triangles?

In triangles, the length of a side opposite to the biggest angle is the longest side, the side opposite to the smallest angle is the shortest side, and the side opposite the medium-angle is of medium length.

What are the properties of exterior angles of triangles?

The measures of the exterior angles of a triangle are equal to the sum of the measures of the two opposite interior angles.

What is the rule of adding two sides of a triangle?

Two sides of a triangle, when added, must be larger than the 3rd. This has to be true for all sides.

How do you find the hypotenuse, opposite, and adjacent of a triangle?

The hypotenuse is the side that is across from the 90 degree angle. The opposite is the side across from theta, and the adjacent side is the side that touches theta that is not the hypotenuse. The hypotenuse is always the longest side.

What is the correct equation to find Sine, Cosine, and Tangent?

Sine=Opp/Hyp
Cosine=Adj/Hyp
Tangent=Opp/Adj

When do you use inverse sine/cosine/tangent? What is the inverse?

When finding the angle instead of side length. arcsin/arccos/arctan(x). (The slash does NOT mean divide it is to seperate possible terms.)

What is the equation of a circle? What do the letters mean?

(x-h)²+(y-k)²=r². The center is (h, k), radius r.

How do you calculate arc length?

angle/360×2πr

How do you calculate sector area?

angle/360*πr²

What is the formula for circle area?

πr²

What is the formula for circumference?

2πr

What is the rule for the angles of chords and central angles?

The central angle is double the angle of the chord angle. The chord angle is half the central angle.