Question

Is ST parallel to PR

Answer 1

Yes ,ST ll PR

Explanation :

We can find out whether ST ll PR by Side splitter theorem which states that if a line is parallel to a side of the triangle it is formed in ,it would divide the two sides it touches in equal proportions.

In ΔPQR

• In PQ, PS/PQ = (102-45)/45 = 57/45 = 1.27
• In QR, TR/QT = 41.8/33 = 1.27

Since PQ and QR are proportionally divided by ST,thus ST is parallel to PR.

Answer 2

Yes, ST is parallel to PR.

Explanation:

To determine if
`\overline{\sf ST}` is parallel to
`\overline{\sf PR}`, we can use the Triangle Proportionality Theorem.

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally.

Therefore, if line segment ST is parallel to side PR, then ST will divide sides PQ and RQ proportionally.

We can set up a proportion according to the Triangle Proportionality Theorem:

`\sf \overline{PS}:\overline{SQ}=\sf \overline{RT}:\overline{TQ}`

Given that:

• 
  `\sf \overline{PS}=102-45=57`
• 
  `\sf \overline{SQ}=45`
• 
  `\sf \overline{RT}=41.8`
• 
  `\sf \overline{TQ}=33`

Substitute these values into the proportion:

`\begin{aligned}\sf \overline{PS}:\overline{SQ}&=\sf \overline{RT}:\overline{TQ}\\\\57:45&=41.8:33\\\\(57)/(45)&=(41.8)/(33)\\\\(57/ 3)/(45/ 3)&=(41.8 / 2.2)/(33/ 2.2)\\\\(19)/(15)&=(19)/(15)\end{aligned}`

As both sides of the equation are the same, it proves that
`\overline{\sf ST}` is parallel to
`\overline{\sf PR}`.