Pythagorean Theorem on the Grid

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square. Which of these squares do NOT support this statement?

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• The number of tiles needed to cover Region X is the same as the number of tiles needed to cover both Region Y and Region Z.

• The number of tiles needed to cover Region Y is the same as the number of tiles needed to cover both Region X and Region Z.

• The number of tiles needed to cover Region Z is the same as the number of tiles needed to cover both Region X and Region Y.

• None of these

• 45.5

• 30

• 32.5

• 6.5

• 37.1 cm

• 40.8 cm

• 27 cm

• 51 cm

• 12

• 14

• 18

• 20

• 8.5 ft

• 10.5 ft

• 9.5 ft

• 13.5 ft

Which measurements could NOT represent the side lengths of a right triangle?

• 6 cm, 8 cm, 10 cm

• 12 cm, 35 cm, 37 cm

• 4 cm, 6 cm, 10 cm

• 10 cm, 24 cm, 26 cm

Point J (-4, -6) and Point K (4, 4) are located on a coordinate grid. Which measurement is closest to the distance between point J and point K in units?

• 18 units

• 6 units

• 13 units

• 9 units

Point M is located at (4, 6) on a coordinate grid. Point M is translated 8 units to the left and 9 units down to create M'. Which measurement is closest to the distance between point M and point M' in units?

• 4 units

• 17 units

• 9 units

• 12 units

• 17

• 10

• 13

• 7