Pythagorean Theorem Converse

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 are the two shorter sides of a right triangle called?

Back

The two shorter sides of a right triangle are called the 'legs'.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, so c = 5.

Front

What type of triangle has one angle that measures 90 degrees?

Back

A right triangle has one angle that measures 90 degrees.

Front

What is the relationship between the sides of an acute triangle?

Back

In an acute triangle, all angles are less than 90 degrees, and the square of the longest side is less than the sum of the squares of the other two sides.

Front

What is the relationship between the sides of an obtuse triangle?

Back

In an obtuse triangle, one angle is greater than 90 degrees, and the square of the longest side is greater than the sum of the squares of the other two sides.

Front

If the sides of a triangle are 5, 12, and 13, is it a right triangle?

Back

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

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

How can you determine if a triangle is a right triangle using the side lengths?

Back

Use the Pythagorean Theorem: if a² + b² = c² holds true for the side lengths, then it is a right triangle.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse states that if a triangle has sides a, b, and c, and a² + b² = c², then the triangle is a right triangle.