Proving Right Triangles/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: 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 6, 8, and 10, is it a right triangle?

Back

Yes, it is a right triangle because 6² + 8² = 10² (36 + 64 = 100).

Front

What are the side lengths of a 5-12-13 triangle?

Back

The side lengths are 5, 12, and 13, which form a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

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

Back

Use the Pythagorean Theorem: check if a² + b² = c², where c is the longest side.

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.

Front

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

Back

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

Front

What is the formula to find the hypotenuse if the other two sides are known?

Back

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

Front

What is an example of a set of lengths that do not form a right triangle?

Back

The lengths 4, 5, and 6 do not form a right triangle because 4² + 5² ≠ 6² (16 + 25 ≠ 36).