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

Option 2.

Reason: V corresponds to Y, and the two sides around ∠V are VU and VW while the two sides around ∠Y are YX and YZ. Compute the ratios:

VU / YX = 50 / 40 = 5/4,
VW / YZ = 60 / 48 = 5/4.

Those two side ratios are equal and ∠V ≅ ∠Y (given), so by the SAS similarity theorem the triangles are similar.