Pythagorean Theorem

A right triangle has a right angle (90º) and two acute angles.

Right Triangle

The hypotenuse is the side opposite the right angle and is the largest side of the triangle.

The legs or catheti (singular: cathetus) are the sides opposite the acute angles and are the shorter sides of the triangle.

Pythagorean Theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.

Pythagorean Theorem

Pythagorean Theorem Formula

Pythagorean Theorem Formula

Formula of Pythagorean Theorem


Examples

Determine whether the following triangle is a right triangle:

Right Triangle

formulas

The legs of a right triangle measure at 3 m and 4 m. What is the length of the hypotenuse?

Right Triangle

Right Triangle Operations

The hypotenuse of a right triangle is 5 m and one of its legs is 3 m. What is the length of the other leg?

Right Triangle

Right Triangle Operations


Problems

A ladder 10 m long is leaning against a wall. The foot of the ladder is 6 m from the base of the wall. At what height does the ladder rest on the wall?

Right Triangle



Right Triangle Operations


Find the area of the equilateral triangle:

Equilateral Triangle

Triangle Operations

Triangle Operations

Triangle Operations


Find the diagonal of the square:

Diagonal of a Square

Triangle Operations

Triangle Solution


Find the diagonal of the rectangle:

Diagonal of a Rectangle

Triangle Operations

Triangle Solution


Find the perimeter and area of the right trapezoid:

Right Trapezoid

Triangle Operations

Triangle Operations

P = 8 + 6 + 12 + 6.32 = 32.32 cm

Triangle Solution


The perimeter of an isosceles trapezoid is 110 m, the bases are 40 and 30 m respectively. Calculate the length of the non-parallel sides and the area.

Isosceles Trapezoid

Triangle Operations

Triangle Operations

Triangle Solution


Find the area of the regular pentagon:

Regular Pentagon

Polygon Operations

Polygon Operations

Polygon Solution


Calculate the area of the square inscribed in a circle with a circumference of 18.84 m.

Square Inscribed in a Circle

Polygon Operations

Polygon Operations

Polygon Solution


In a circle a chord of 48 cm is 7 cm from the center. Calculate the area of the circle.

Chord of a Circle

Polygon Operations

Polygon Solution