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 are the side lengths of a right triangle?

Back

In a right triangle, the side lengths are typically referred to as 'a' and 'b' for the two legs, and 'c' for the hypotenuse.

Front

If a triangle has sides of lengths 9, 12, and 15, is it a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if a² + b² = c² holds true for the side lengths.

Front

What is the value of the missing side if one side is 6.5 cm and the hypotenuse is 10 cm?

Back

Using the Pythagorean Theorem: 6.5² + b² = 10², b = 8.5 cm.

Front

What is the value of the missing side if one side is 17.9 cm and the hypotenuse is 20 cm?

Back

Using the Pythagorean Theorem: 17.9² + b² = 20², b = 6.8 cm.

Front

What does it mean if a triangle's sides are 30, 60, and 90?

Back

A triangle with sides 30, 60, and 90 is not a right triangle because 30² + 60² does not equal 90².

Front

Can a triangle with sides 6, 8, and 9 be a right triangle?

Back

No, it does not satisfy the Pythagorean Theorem since 6² + 8² ≠ 9².

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

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).