Question

what value of x will make △onm similar to △srq by the sas similarity theorem? 16 20 25 50

Explanation:

Step1: Apply SAS similarity theorem

For \(\triangle ONM\sim\triangle SRQ\) by SAS similarity theorem, \(\frac{ON}{SR}=\frac{MN}{QR}\).
Given \(ON = 8\), \(SR=20\), \(MN = 10\), and \(QR=x\).
So, \(\frac{8}{20}=\frac{10}{x}\).

Step2: Solve the proportion

Cross - multiply: \(8x=20\times10\).
\(8x = 200\).
Divide both sides by 8: \(x=\frac{200}{8}=25\).

Answer:

25