Question

ii vx = wz = 40 cm and m∠zv x = m∠xwz = 22°, can δvzx and δwxz be proven congruent by sas? why or why not?
○ yes, along with the given information, \\(\overline{zx} \cong \overline{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: Identify given info

Given: $VX = WZ = 40$ cm, $\angle ZVX = \angle XWZ$. Need to check SAS for $\triangle VZX$ and $\triangle WXZ$.

Step2: Check SAS conditions

SAS requires two sides and included angle. For $\triangle VZX$: sides $VX, ZX$ and included $\angle ZVX$. For $\triangle WXZ$: sides $WZ, ZX$ and included $\angle XWZ$. $VX=WZ$, $\angle ZVX=\angle XWZ$, but $ZX$ is common (reflexive property: $ZX=ZX$). So SAS conditions are met.

Answer:

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