Question

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

ZY ∥ WX
∠Z ≅ ∠Y and ∠W ≅ ∠X
ZV ≅ VY and WV ≅ VX
∠Z ≅ ∠X and ∠W ≅ ∠Y

Answer 1

option d is correct because only then similarity criterion will be applied.

all angles of similar traingles are equal.

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Answer 2

The correct relationship is ∠Z ≅ ∠X and ∠W ≅ ∠Y.

• To be associated with two numbers, each called angle will conform to and be congruent with ONE other angle. If you have ZYV and XWV, Z must conform to X as they both first appear in the order.

        Thus,

        ∠Z≅∠X

         ∠V≅∠V

        ∠Y≅∠W

• Our first solution choice is linked to parallelism, which does not affect whether or not certain angles are congruent.
• For the second response alternative, ∠Z is congruent to ∠X and not with ∠Y, hence it is incorrect.
• For the third answer alternative, it indicates that ∠Z will equate to ∠V, but it does not, so it is also incorrect.
• For option D, since ∠Z is congruent to ∠X, and ∠W is congruent to ∠Y, it is true.

Therefore, the relation ∠Z ≅ ∠X and ∠W ≅ ∠Y is correct.