Pythagorean Theorem and 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 is a right triangle?

Back

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

Front

What is the hypotenuse of 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 obtuse, acute, or right using side lengths?

Back

Use the Pythagorean Theorem: If a² + b² = c², the triangle is right; if a² + b² > c², it is obtuse; if a² + b² < c², it is acute.

Front

What are the conditions for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 4, 5, and 6, what type of triangle is it?

Back

It is an acute triangle.

Front

If a ladder is placed 10 feet away from a house and needs to reach 25 feet high, how tall must the ladder be?

Back

The ladder must be 27 feet tall.

Front

In a right triangle with sides 30, 40, and 50, which side is the hypotenuse?

Back

The hypotenuse is 50.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse.

Front

If a triangle has sides of lengths 15, 8, and 4, can it form a triangle?

Back

No, it cannot form a triangle (Not a Triangle).