Models with Pythagorean Theorem

If the area of square c is 1,369 cm² and the area of square b is 1,225 cm², what is the length of one side of square a?

• 12 cm

• 144 cm

• 50.9 cm

• 8.5 cm

What is the area of square b in the figure shown?

• 24 in²

• 96.6 in²

• 74 in²

• 576 in²

What letter represents the hypotenuse?

• a

• b

• a and b

• c

In the converse Pythagorean theorem, if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is:

• right triangle

• scalene triangle

• equilateral triangle

• isosceles triangle

If a triangle has side lengths 9, 12, and 15, is it a right triangle according to the converse Pythagorean theorem?

• Yes

• No

• Maybe

• I'm not sure

Which of the following statements is true about the converse Pythagorean theorem?

• The converse Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

• The converse Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the product of the squares of the lengths of the other two sides, then the triangle is a right triangle.

• The converse Pythagorean theorem states that if the sum of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle.

• The converse Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the difference of the squares of the lengths of the other two sides, then the triangle is a right triangle.

If a triangle has side lengths 8, 15, and 17, is it a right triangle according to the converse Pythagorean theorem?

• No

• Yes

• Maybe

• I'm not sure

Which of the following statements represents the converse Pythagorean theorem?

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

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

• If the triangle is not a right triangle, then the square of the length of one side of the triangle is equal to the sum of the squares of the other two sides.

• If the triangle is a right triangle, then the square of the length of one side of the triangle is not equal to the sum of the squares of the other two sides.

Which of the following triangles satisfies the converse Pythagorean theorem?

• Scalene triangle

• Isosceles triangle

• Equilateral triangle

• Right triangle

If a triangle has side lengths 7, 10, and 12, is it a right triangle according to the converse Pythagorean theorem?

• Maybe

• Yes

• No

• I don't know