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). It can be expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

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

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the hypotenuse is always the longest side.

Front

True or False: The Pythagorean Theorem can be used for all types of triangles.

Back

False. The Pythagorean Theorem only applies to right triangles.

Front

What is the formula for the Pythagorean Theorem?

Back

The formula is a² + b² = c².

Front

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

Back

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

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

How can you determine if a triangle is acute, right, or obtuse using side lengths?

Back

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