Pythagorean Theorem & Converse

Front

What does the Pythagorean Theorem state?

Back

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): a² + b² = c².

Front

What is the converse of the Pythagorean Theorem?

Back

If a² + b² = c² is true for a triangle, then the triangle is a right triangle.

Front

What type of triangle is formed if a² + b² < c²?

Back

An obtuse triangle.

Front

What type of triangle is formed if a² + b² > c²?

Back

An acute triangle.

Front

What is the length of the diagonal of a rectangle with sides 5 yards and 12 yards?

Back

13 yards.

Front

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

Back

It is a right triangle.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

Check if a² + b² = c² holds true for the side lengths.

Front

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

Back

Two sides are of equal length, and the angles opposite those sides are equal.

Front

In a right triangle, what is the hypotenuse?

Back

The longest side opposite the right angle.

Front

What is the formula to find the length of the diagonal in a rectangle?

Back

Diagonal = √(length² + width²).