Questions: Consider ΔWXY and ΔBCD with ∠X ≅ ∠C, WX ≅ BC, and WY ≅ BD. Can it be concluded that ΔWXY ≅ ΔBCD by SAS? Why or why not?

Solution Steps

We are given that:

• ∠X ≅ ∠C
• WX ≅ BC
• WY ≅ BD

The Side-Angle-Side (SAS) criterion for triangle congruence states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

In the given information:

• ∠X and ∠C are corresponding angles.
• WX and BC are corresponding sides.
• WY and BD are corresponding sides.

However, the angle given (∠X ≅ ∠C) is not the included angle between the given sides (WX and WY in ΔWXY, and BC and BD in ΔBCD).

Final Answer