Question

The figure shows three quadrilaterals on a coordinate grid:

Which of the following statements is true about the three quadrilaterals?

M and O are similar and congruent.
O and N are similar and congruent.
M and N are similar but not congruent.
M and O are similar but not congruent.

Answer 1

D. M and O are similar but not congruent.

Explanation:

To begin, let's eliminate some options.

It can't be A. M and O are similar and congruent because M and O aren't congruent because they are different sizes. It cannot be B. O and N are similar and congruent because they aren't congruent since they're different sizes. Lastly, it cannot be C. M and N are similar but not congruent, because these two are actually congruent.

Therefore, the correct answer is D. M and O are similar but not congruent.

Answer 2

Option D.

Explanation:

From the given figure it is clear that the three quadrilaterals on a coordinate grid are squares because all sides of each quadrilaterals are same and all interior angles are right angles.

Side length of square M = 2 units

Side length of square N = 2 units

Side length of square O = 4 units

The corresponding sides of congruent figures are congruent. So,

Square M ≅ Square N

The corresponding sides of similar figures are proportional. So,

Square M
`\sim` Square N

Square M
`\sim` Square O

Square N
`\sim` Square O

M and O are similar but not congruent.

Therefore, the correct option is D.