Question

The figure below shows three quadrilaterals on a coordinate grid:

A coordinate grid is shown from positive 8 to negative 8 on the x axis and from positive 8 to negative 8 on the y axis. An image of a rectangle labeled E is shown on ordered pair negative 1, negative 1 and negative 3, negative 1 and negative 3, negative 2 and negative 1, negative 2. Another image of a rectangle labeled G is shown on ordered pair negative 2, negative 2 and negative 6, negative 2 and negative 6, negative 4 and negative 2, negative 4. Another image of a rectangle labeled F is shown on ordered pair negative 1, 1 and negative 1, 2, and negative 3, 2 and negative 3, 1.

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

E and F are similar but not congruent.
E and G are similar but not congruent.
G and F are similar and also congruent.
E and G are similar and also congruent.

Answer 1

(a) A and B are similar but not congruent

Explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

A and B are similar, but not congruent.