Given two triangles, $△\mathrm{ONM}$ and $△\mathrm{SRQ}$, where side $\mathrm{ON}$ corresponds to $\mathrm{SR}$ and side $\mathrm{NM}$ corresponds to $\mathrm{RQ}$, if $\mathrm{ON}=16$, $\mathrm{NM}=x$, $\mathrm{SR}=20$, and $\mathrm{RQ}=25$, what value of $x$ will make the triangles similar by the SAS similarity theorem?

• A. $50$
• B. $20$
• C. $16$
• D. $25$

Answer: (D)

Verified step by step guidance

1. Recall the SAS (Side-Angle-Side) similarity theorem: two triangles are similar if two pairs of corresponding sides are proportional and the included angles between those sides are equal.
2. Identify the pairs of corresponding sides given: side ON corresponds to side SR, and side NM corresponds to side RQ. We are given ON = 16, SR = 20, NM = x, and RQ = 25.
3. Set up the proportion for the pairs of corresponding sides to be equal, since similarity requires the ratios of corresponding sides to be the same: \(\frac{ON}{SR} = \frac{NM}{RQ}\).
4. Substitute the known values into the proportion: \(\frac{16}{20} = \frac{x}{25}\).
5. Solve the proportion for \(x\) by cross-multiplying: \$16 \times 25 = 20 \times x\(, then isolate \)x$ by dividing both sides by 20.