Question

if vx = wz = 40 cm and m∠zvx = m∠xwz = 22°, can δvzx and δwxz be proven congruent by sas? why or why not? yes, along with the given information, zx ≅ zx by the reflexive property. yes, the triangles are both obtuse. no, the sides of the triangles intersect. no, there is not enough information given.

Explanation:

Step1: Recall SAS congruence criterion

SAS (Side - Angle - Side) requires two sides and the included angle of one triangle to be congruent to two sides and the included angle of another triangle.

Step2: Identify given information

We are given that $VX = WZ=40$ cm and $\angle ZVX=\angle XWZ = 22^{\circ}$. Also, $\overline{ZX}=\overline{ZX}$ by the reflexive property.

Step3: Check for SAS

In $\triangle VZX$ and $\triangle WXZ$, we have side $VX = WZ$, $\angle ZVX=\angle XWZ$ and side $ZX$ is common to both triangles. The angle is the included - angle between the two sides in both triangles. So, the triangles are congruent by SAS.

Answer:

Yes, along with the given information, $\overline{ZX}\cong\overline{ZX}$ by the reflexive property.