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). It is expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

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 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 obtuse, acute, or right using side lengths?

Back

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

Front

Given sides 9, 12, and 17, does it form a right triangle?

Back

No, because 9² + 12² = 81 + 144 = 225, and 17² = 289. (225 < 289, so it's obtuse).

Front

What is the distance between two points using the Pythagorean Theorem?

Back

The distance can be found by treating the two points as the endpoints of a right triangle, where the legs are the differences in x and y coordinates.

Front

If a right triangle has legs of lengths 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is an example of an obtuse triangle?

Back

A triangle with sides of lengths 3, 4, and 6 is obtuse because 3² + 4² < 6² (9 + 16 < 36).

Front

What is an acute triangle?

Back

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