Pythag 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

How can 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 the squares of the lengths of the two shorter sides add up to the square of the length of the longest side.

Front

What is an acute triangle?

Back

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

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is a right triangle?

Back

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

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25, which is equal to 5².

Front

If a triangle has sides of lengths 2, 2, and 3, is it acute, obtuse, or right?

Back

It is an obtuse triangle because 2² + 2² < 3² (4 + 4 < 9).

Front

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

Back

It is a right triangle because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.