Converse of Pythagorean Theorem

Front

What is the Converse of the Pythagorean Theorem?

Back

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

How can you determine if a triangle is acute using side lengths?

Back

If the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.

Front

How can you determine if a triangle is obtuse using side lengths?

Back

If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse.

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the lengths of the sides must satisfy the equation a² + b² = c², where c is the length of the hypotenuse.

Front

Can the side lengths 3, 4, and 5 form a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

Front

Can the side lengths 11, 12, and 15 form a right triangle?

Back

No, because 11² + 12² = 121 + 144 = 265, which is not equal to 15² (225).

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 where one angle is greater than 90 degrees.

Front

If a triangle has sides of lengths 4, 8, and 10, what type of triangle is it?

Back

It is an obtuse triangle because 10² > 4² + 8² (100 > 16 + 64).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.