Question

given the similar polygons in the image, which statement is true?
(overline{dg}congoverline{us})
(angle dcongangle n)
(overline{do}congoverline{un})
(angle scongangle g)

Explanation:

Step1: Recall the property of similar polygons

Similar polygons have corresponding angles congruent.

Step2: Identify corresponding angles

In similar polygons (here triangles as they are polygons with 3 sides), the angles that are in the same relative position are congruent. For Figure A (\(\triangle DGO\)) and Figure B (\(\triangle NSU\)), \(\angle D\) in Figure A and \(\angle N\) in Figure B are in the same relative position. So, \( \angle D\cong\angle N \) by the property of similar polygons.

Step3: Analyze other options

• For \( \overline{DG}\cong\overline{US} \): Since the polygons are similar (not necessarily congruent), sides are in proportion (\(\frac{DG}{NS}=\frac{GO}{SU}=\frac{OD}{UN}\)) but not necessarily equal.
• For \( \overline{DO}\cong\overline{UN} \): Again, similar polygons have sides in proportion, not necessarily equal.
• For \( \angle S\cong\angle G \): \(\angle S\) and \(\angle G\) are not corresponding angles (based on the structure of similar polygons where angles match in order of similarity).

Answer:

B. \( \angle D\cong\angle N \)