Pythagorean Theorem Basics

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If one side of a right triangle is 24 and the other is 32, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 24² + 32²; c² = 576 + 1024; c² = 1600; c = 40.

Front

Can the sides 10, 8, and 6 form a right triangle?

Back

Yes, because 10² = 8² + 6² (100 = 64 + 36).

Front

What is the condition for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

Can the sides 7, 8, and 9 form a triangle?

Back

No, because 7 + 8 is not greater than 9.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the legs of a right triangle?

Back

The legs are the two sides that form the right angle.

Front

If a triangle has sides of lengths 15, 8, and 17, can it be a right triangle?

Back

Yes, because 17² = 15² + 8² (289 = 225 + 64).

Front

What is the formula to find the length of the hypotenuse?

Back

c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.