Proof and Converse of Pythagorean Theorem

Which equation is modeled by the picture shown?

• 3²+5²=4²

• 3²+4²=5²

• 5²+4²=3²

• 9²+16²=25²

Is this triangle a right triangle? (Picture not drawn to scale)

• yes

• no

What is the area of the third square?

• 6.7 cm²

• 33.5 cm²

• 2025 cm²

• 45 cm²

If the area of the blue square is 25 in² and the area of the green square is 169 in², what is the area of the yellow square?

• 12 in²

• 144 in²

• 194 in²

• 13.9 in²

Find the value of x. Round your answer to the nearest tenth.

Mathematical Equivalence

ON

Find the value of x.

Mathematical Equivalence

ON

A model of the Pythagorean Theorem is shown. Which statement is true?

• If you add the areas of regions R and P they will add to the area of region Q

• If you add areas of regions R and Q they will add to the area of region P

• If you subtract the areas of regions Q and R they will make the area of region P

Which of the following sentences would belong in the proof that describes this image?

• The sum of the areas of the two smaller squares is equal to the area of the large square.

• The sum of the side lengths of the two smaller squares is equal to the side length of the large square.

• The difference of the areas of the two smaller squares is equal to the area of the large square.

• The differences of the side lengths of the two smaller squares is equal to the side length of the large square.

Which equation will help you find the length of c?

Calculate the length of the hypotenuse.

• 23.1 cm

• 30.4 cm

• 41 cm

• 1681 cm