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 SSS similarity theorem?

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.
Show that the ratios StartFraction U V Over Z Y EndFraction , StartFraction W U Over Z X EndFraction , and StartFraction W V Over X Y EndFraction are equivalent.
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 V Over Z Y EndFraction and StartFraction W U Over Z X EndFraction are equivalent, and ∠U ≅ ∠Z.

Answer 1

(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.

`(UW)/(XZ)=(WV)/(ZY)=(UV)/(XY)`

Explanation:

In Triangles WUV and XZY:

`\angle VUW$ and \angle YXZ$ are congruent. \\\angle U W V$ and \angle X Z Y$ are congruent.\\ \angle U V W$ and \angle Z Y X$ are congruent.`

Therefore:

`\triangle UWV \cong \triangle XZY`

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

`(UW)/(XZ)=(WV)/(ZY)=(UV)/(XY)`

As a check:

`(UW)/(XZ)=(40)/(32)=1.25\\\\(WV)/(ZY)=(60)/(48)=1.25\\\\(UV)/(XY)=(50)/(40)=1.25`

The correct option is A.