Right Triangle Properties and Theorems

Front

What is a right triangle?

Back

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

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): a² + b² = c².

Front

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

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

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

Back

Yes, because 5² + 12² = 25 + 144 = 169, which equals 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

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

Can a triangle with sides 14, 15, and 29 be a right triangle?

Back

No, because 14² + 15² = 196 + 225 = 421, which does not equal 29² (841).

Front

What is the classification of a triangle with sides 9, 40, and 41?

Back

It is a right triangle because 9² + 40² = 81 + 1600 = 1681, which equals 41².