Question

In addition to the information given in the drawing, which statement would be sufficient to prove

that STW-XYZ?

Number 5

Answer 1

`SW= 15` and
`TW= 24`

Step-by-step explanation:

Given

See attachment for the triangles

Required

Which additional statement proves the similarity of both triangles

From the attachment:

`ST = 27\\XY = 9\\YZ = 8\\XZ = 5`

The similar sides of both triangles are: ST and XY

So:

`Ratio = ST : XY`

`Ratio = 27 : 9`

Divide by 9

`Ratio = 3 : 1`

Another similar sides are: TW and YZ

So:

`TW : YZ = TW : 8`

Equate both ratios:

`TW : 8 = 3 : 1`

Represent as fraction

`(TW )/( 8 )= (3 )/( 1)`

`(TW )/( 8 )= 3`

Multiply both sides by 8

`8 * (TW )/( 8 )= 3*8`

`TW= 3*8`

`TW= 24`

Another similar sides are: SW and XZ

So:

`SW:XZ = SW:5`

Equate both ratios:

`SW:5 = 3:1`

Represent as fraction

`(SW)/(5) = (3)/(1)`

`(SW)/(5) = 3`

Multiply both sides by 5

`5*(SW)/(5) = 3*5`

`SW = 3*5`

`SW = 15`

So, the statement that proves the similarity of the triangles is:

`SW= 15` and
`TW= 24`