Question

(02.05)The figure shows three quadrilaterals on a coordinate grid:

A coordinate plane is shown. Quadrilateral D has sides measuring 3 units and 1 unit. Quadrilateral F has sides measuring 3 units and 1 unit. Quadrilateral E has sides measuring 2 units and 6 units.

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

A. D and E are similar but not congruent.
B. E and F are similar and congruent.
C. D and E are similar and congruent.
D. F and D are similar but not congruent.

Answer 1

A. D and E are similar but not congruent.

Explanation:

The side lengths of D are 3 units and 1 unit. The side lengths of E are 2 units and 6 units. The sides are proportional, but are not congruent; this means that the quadrilaterals are similar but not congruent. Choice A is true and choice C is false.

The side lengths of E are 2 units and 6 units. The side lengths of F are 3 units and 1 unit. The sides are proportional, but are not congruent; this means that the quadrilaterals are similar but not congruent. Choice B is false.

The side lengths of D are 3 units and 1 unit. The side lengths of F are 3 units and 1 unit. The sides are congruent; this means that the quadrilaterals are congruent. Choice D is false.