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). Formula: c² = a² + b².

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 = 3 and b = 4, what is c?

Back

c = 5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

What type of triangle has one angle greater than 90 degrees?

Back

An obtuse triangle.

Front

In a right triangle, if one side is 6 and the hypotenuse is 10, what is the length of the other side?

Back

The other side is 8 (using the Pythagorean Theorem: 6² + b² = 10², so 36 + b² = 100, b² = 64, b = 8).

Front

True or False: The hypotenuse can be shorter than either of the other two sides in a right triangle.

Back

False.

Front

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

Back

The sum of the squares of the two shorter sides equals the square of the hypotenuse.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

If a = 8 and c = 10, what is b?

Back

b = 6 (using the Pythagorean Theorem: 8² + b² = 10², so 64 + b² = 100, b² = 36, b = 6).