Question

Complete the similarity statement for the two quadrilaterals given.

Enter your answer in the box.

quadrilateral PGYX∼quadrilateral

Answer 1

The complete similarity statement for the two quadrilaterals is: quadrilateral PGYX ⋍ quadrilateral WDQA.

In order to establish the similarity between quadrilaterals PGYX and WDQA, we need to identify corresponding angles and corresponding side lengths. Corresponding angles in similar polygons are those that share the same relative positions within their respective polygons. In this case, we can observe the following corresponding angles:

∠P corresponds to ∠W

∠G corresponds to ∠D

∠Y corresponds to ∠Q

∠X corresponds to ∠A

Since corresponding angles in similar polygons are congruent, we can conclude that:

∠P ≅ ∠W

∠G ≅ ∠D

∠Y ≅ ∠Q

∠X ≅ ∠A

Now, let's analyze the corresponding side lengths. Corresponding side lengths in similar polygons are those that connect corresponding angles. In this case, we can identify the following corresponding side lengths:

PG corresponds to WD

GY corresponds to DQ

YX corresponds to QA

PX corresponds to AW

To establish the similarity between quadrilaterals PGYX and WDQA, we need to demonstrate that the ratios of corresponding side lengths are equal. We can do this by calculating these ratios:

PG/WD = GY/DQ = YX/QA = PX/AW

If these ratios are all equal, then the corresponding side lengths are proportional, and the quadrilaterals are similar. Therefore, the complete similarity statement for the two quadrilaterals is:

quadrilateral PGYX ⋍ quadrilateral WDQA.

Answer 2

[ quadrilateral PGYX∼quadrilateral WDQA ]

In all polygons, both are to be similar if all the angles are correspoding with each other. In these two quadrilateral's the angles PGYX correspond with the angles WDQA.

∠P =∠W

∠G =∠D

∠Y =∠Q

∠X =∠A

Best of Luck!