Question

Which must be true in order for the relationship △ZYV ~ △XWV to be correct?

a. ZY ∥ WX

b. ∠Z ≅ ∠Y and ∠W ≅ ∠X

c. ZV ≅ VY and WV ≅ VX

d. ∠Z ≅ ∠X and ∠W ≅ ∠Y

Answer 1

The answer would be D, d. ∠Z ≅ ∠X and ∠W ≅ ∠Y

Answer 2

Hey there!

In order for two figures to be congruent, each named angle must correspond and be congruent to ONE other angle. If you have ZYV and XWV, Z must be congruent to X as they both show up first in the ordering.

This means...

∠Z≅∠X

∠Y≅∠W

∠V≅∠V

Our first answer option has to do with parallelism, which does not influence if certain angles are congruent or not.

For the second answer option, ∠Z is congruent to ∠X, not ∠Y, so it is incorrect.

For the third answer option, it shows that ∠Z would correspond to ∠V, but it does not, so it is also incorrect.

For D, ∠Z IS congruent to ∠X, and ∠W IS congruent to ∠Y

Therefore, our answer is D) ∠Z≅∠X and ∠W ≅ ∠Y.

I hope this helps!