Pythagorean Theorem
A right triangle has a right angle (90º) and two acute angles.
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.
Examples
Determine whether the following triangle is a right triangle:
The legs of a right triangle measure at 3 m and 4 m. What is the length of the hypotenuse?
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?
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?
Find the area of the equilateral triangle:
Find the diagonal of the square:
Find the diagonal of the rectangle:
Find the perimeter and area of the right trapezoid:
P = 8 + 6 + 12 + 6.32 = 32.32 cm
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.
Find the area of the regular pentagon:
Calculate the area of the square inscribed in a circle with a circumference of 18.84 m.
In a circle a chord of 48 cm is 7 cm from the center. Calculate the area of the circle.
