Question

proving triangle congruence
given ( overline { v w } cong overline { x w } ) and ( angle v w y cong angle x w y ), prove that ( \triangle v y w cong \triangle x y w ).
( angle s t w cong angle u t v ) because they are ang
( \triangle w s t cong \triangle v u t ) using the triangle c
theorem.
given ( overline { c e } ) is a perpendicular bisector of ( overline { f d } ), prove that ( \triangle f e c cong )

Explanation:

Step1: Analyze the given information

We are given that $\overline{VW}\cong\overline{XW}$ (side), $\angle VWY\cong\angle XWY$ (angle), and $\overline{WY}$ is common to both $\triangle VYW$ and $\triangle XYW$ (side).

Step2: Apply the SAS (Side - Angle - Side) congruence criterion

In $\triangle VYW$ and $\triangle XYW$:

• $VW = XW$ (given)
• $\angle VWY=\angle XWY$ (given)
• $WY = WY$ (common side)

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

Answer:

$\triangle VYW\cong\triangle XYW$ by the SAS (Side - Angle - Side) congruence criterion.