Using the Pythagorean Theorem

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 a right triangle?

Back

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

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, it is a right triangle because 3² + 4² = 5² (9 + 16 = 25).

Front

How can you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the relationship is defined by the Pythagorean Theorem: a² + b² = c².

Front

Can the lengths 20, 25, and 15 form a right triangle?

Back

Yes, because 15² + 20² = 25² (225 + 400 = 625).

Front

What does it mean if a triangle is not a right triangle?

Back

If a triangle is not a right triangle, it means that none of its angles measure 90 degrees.

Front

True or False: The sides 12, 5, and 13 can form a right triangle.

Back

True, because 5² + 12² = 13² (25 + 144 = 169).

Front

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

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).