Question

Consider the two triangles. Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32. How can the triangles be proven similar by the SAS similarity theorem? Show that the ratios StartFraction X Y Over V U EndFraction and StartFraction Y Z Over V W EndFraction are equivalent, and ∠U ≅ ∠X. Show that the ratios StartFraction U V Over X Y EndFraction and StartFraction W V Over Z Y EndFraction are equivalent, and ∠V ≅ ∠Y. Show that the ratios StartFraction U W Over Z X EndFraction and StartFraction X Y Over W V EndFraction are equivalent, and ∠W ≅ ∠X. Show that the ratios StartFraction X Z Over W U EndFraction and StartFraction Z Y Over W V EndFraction are equivalent, and ∠U ≅ ∠Z.

Answer 1

Answer: The answer is A

Explanation:

Answer 2

Explanation:

(A)Show that the ratios StartFraction U V Over X Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over Z Y EndFraction are equivalent.

Explanation:

In Triangles WUV and XZY:

Therefore:

To show that the triangles are similar by the SSS similarity theorem, we have:

As a check:

The correct option is A.