Pythagorean Theorem and Converse without inequalities

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: c² = a² + b².

Front

What is a right triangle?

Back

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

Front

How do you identify 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, because 3² + 4² = 5² (9 + 16 = 25).

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).

Front

Calculate the length of the hypotenuse for a triangle with sides 6 and 8.

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 25² (49 + 576 = 625).

Front

What is the formula to find the length of one side of a right triangle if the other two sides are known?

Back

To find the length of one side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

In a right triangle, if one side is 12 and the hypotenuse is 13, what is the length of the other side?

Back

Using the Pythagorean Theorem: b² = 13² - 12²; b² = 169 - 144; b² = 25; b = 5.