James cut out four parallelograms, the dimensions of which are shown below.
Parallelogram 1
length: 12 in.
width: 15 in.
diagonal: 20 in.
Parallelogram 2
length: 16 in.
width: 30 in.
diagonal: 34 in.
Parallelogram 3
length: 20 in.
width: 21 in.
diagonal: 29 in.
Parallelogram 4
length: 18 in.
width: 20 in.
diagonal: 26 in.
James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle.
4 parallelograms are put together so that one vertex from each paper exists on a point.
Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply.
The quadrilaterals can be placed such that each occupies one-quarter of the circle.
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles.
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles.
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
5 answers
The statements "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles," "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles," "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles," and "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles" are false.
Therefore, the answer is "None of the above."
The statement "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles" is true because the diagonals of parallelogram 2 do not form right angles.
The statement "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles" is false because parallelograms do not necessarily have right angles.
The statement "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles" is false because parallelograms do not necessarily have right angles.
Therefore, the only correct statement is "The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles."
3 squares form a triangle. The squares have areas 6 inches squared, 10 inches squared, 8 inches squared.
4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, 16 inches squared.
5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.
6 squares form a triangle. The squares have areas 7 inches squared, 25 inches squared, 24 inches squared.
7 squares form a triangle. The squares have areas 64 inches squared, 225 inches squared, 289 inches squared.
8 squares form a triangle. The squares have areas 10 inches squared, 26 inches squared, 24 inches squared.
Using this information, we can determine which triangles are right triangles:
For the first triangle: 6^2 + 8^2 = 10^2, which satisfies the Pythagorean theorem. Therefore, the first triangle is a right triangle.
For the second triangle: 9^2 + 16^2 ≠ 25^2, so it does not satisfy the Pythagorean theorem. Therefore, the second triangle is not a right triangle.
For the third triangle: 25^2 + 144^2 = 169^2, which satisfies the Pythagorean theorem. Therefore, the third triangle is a right triangle.
For the fourth triangle: 7^2 + 24^2 ≠ 25^2, so it does not satisfy the Pythagorean theorem. Therefore, the fourth triangle is not a right triangle.
For the fifth triangle: 64^2 + 289^2 ≠ 225^2, so it does not satisfy the Pythagorean theorem. Therefore, the fifth triangle is not a right triangle.
For the sixth triangle: 10^2 + 24^2 = 26^2, which satisfies the Pythagorean theorem. Therefore, the sixth triangle is a right triangle.
Based on the above analysis, the three triangles that are right triangles are the first, third, and sixth triangles.