Answer:
[tex]SW= 15[/tex] and [tex]TW= 24[/tex]
Step-by-step explanation:
Given
See attachment for the triangles
Required
Which additional statement proves the similarity of both triangles
From the attachment:
[tex]ST = 27\\XY = 9\\YZ = 8\\XZ = 5[/tex]
The similar sides of both triangles are: ST and XY
So:
[tex]Ratio = ST : XY[/tex]
[tex]Ratio = 27 : 9[/tex]
Divide by 9
[tex]Ratio = 3 : 1[/tex]
Another similar sides are: TW and YZ
So:
[tex]TW : YZ = TW : 8[/tex]
Equate both ratios:
[tex]TW : 8 = 3 : 1[/tex]
Represent as fraction
[tex]\frac{TW }{ 8 }= \frac{3 }{ 1}[/tex]
[tex]\frac{TW }{ 8 }= 3[/tex]
Multiply both sides by 8
[tex]8 * \frac{TW }{ 8 }= 3*8[/tex]
[tex]TW= 3*8[/tex]
[tex]TW= 24[/tex]
Another similar sides are: SW and XZ
So:
[tex]SW:XZ = SW:5[/tex]
Equate both ratios:
[tex]SW:5 = 3:1[/tex]
Represent as fraction
[tex]\frac{SW}{5} = \frac{3}{1}[/tex]
[tex]\frac{SW}{5} = 3[/tex]
Multiply both sides by 5
[tex]5*\frac{SW}{5} = 3*5[/tex]
[tex]SW = 3*5[/tex]
[tex]SW = 15[/tex]
So, the statement that proves the similarity of the triangles is:
[tex]SW= 15[/tex] and [tex]TW= 24[/tex]
