Question

What additional information is needed to prove the triangles are congruent by the SAS Postulate

Answer 1

Answer:  The correct option is (A) ∠XWY ≅ ∠ZWY.

Step-by-step explanation:  We are given to select the correct additional information that is needed to prove the triangles WXY and WZY are congruent by the SAS Postulate.

From the figure, we notice that

in triangles WXY and WZY, we have

WX ≅ WZ [Given]

WY ≅ WY [Common side to both the triangles]

So, to prove that ΔWXY ≅ ΔWZY by SAS (side-angle-side) postulate, the angle lying between the corresponding pair of sides must be congruent.

In triangle XWZ, angle lying between the sides WX and WY is ∠XWY,

in triangle ZWY, angle lying between the sides WZ and WY is ∠ZWY.

Therefore, we must have

∠XWY ≅ ∠ZWY.

Thus, the correct option is (A) ∠XWY ≅ ∠ZWY.

Answer 2

To prove the SAS (side-angle-side) postulate, a. <XWY=<ZWY needs to be marked congruent. Since the segment WY=WY due to the reflexive property, we need an angle between them to prove SAS, which has to be XWY and ZWY.