If x is the midpoint of line vy and wz and the reason is given then wx=xz and vx=xy then angle wxv = angle yzx to get the triangle vwx congruent to triangle yzx then what would be the reasons after given to make the triangle congruent
SAS
To prove that triangle VWX is congruent to triangle YZX, you need to show that all three pairs of corresponding sides and angles are congruent. Here are the reasons after the given statements to make the triangles congruent:
1. WX = XZ (given: x is the midpoint of line VW and WZ)
2. VX = XY (given: x is the midpoint of line VW and WZ)
3. WV = ZY (given: x is the midpoint of line VW and WZ, so WV = VZ and WY = ZX by definition of midpoint)
4. angle WXV = angle YXZ (vertical angles are congruent)
5. angle VWX = angle YZX (given: WX = XZ and VX = XY)
6. angle WVX = angle ZYX (given: WV = ZY and VX = XY)
By showing that the sides and angles of the two triangles are congruent, we can conclude that triangle VWX is congruent to triangle YZX.