Question

the graph shows quadrilaterals efgh and opqr. is efgh congruent to opqr? justify your answer. yes, because a rotation 90° counterclockwise around the origin maps efgh onto opqr. yes, because a translation right 10 units and down 2 units maps efgh onto opqr. no, because ∠g and ∠q do not have the same measure. no, because $overline{he}$ and $overline{ro}$ do not have the same length.

Explanation:

Step1: Recall congruence criteria

Congruent figures have same shape and size, corresponding sides and angles are equal.

Step2: Analyze rotation

A 90 - degree counter - clockwise rotation around the origin has the transformation rule $(x,y)\to(-y,x)$. By visually inspecting and applying transformation rules, we can see that a 90 - degree counter - clockwise rotation around the origin maps EFGH onto OPQR.

Step3: Analyze translation

If we consider a translation right 10 units and down 2 units, the coordinates of the vertices of EFGH will not match those of OPQR.

Step4: Analyze angles and sides

There is no indication that $\angle G$ and $\angle Q$ have different measures or that $\overline{HE}$ and $\overline{RO}$ have different lengths.

Answer:

Yes, because a rotation 90° counterclockwise around the origin maps EFGH onto OPQR.