Question

essay 14 points. explain why or why not figure abcd is congruent to figure efgh.

Explanation:

Step1: Recall congruence definition

Two figures are congruent if they have the same shape and size, which means corresponding sides and angles are equal.

Step2: Check corresponding side - lengths

We can use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ on the grid (counting unit - lengths). For example, if we find the length of side $AB$ and side $EF$. By counting the horizontal and vertical displacements between the endpoints of the sides on the grid, we can see that the lengths of corresponding sides are not equal.

Step3: Conclusion

Since corresponding side - lengths are not equal, the two figures are not congruent.

Answer:

Figure $ABCD$ is not congruent to figure $EFGH$ because the corresponding side - lengths of the two figures are not equal.