Question

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

Explanation:

Step1: Recall SAS Similarity Theorem

For two triangles to be similar by SAS (Side - Angle - Side) similarity theorem, the ratio of two corresponding sides must be equal and the included angle must be equal. In $\triangle ONM$ and $\triangle SRQ$, the included angles (the angles with the arc) are equal. So we need $\frac{ON}{SR}=\frac{NM}{RQ}$.

We know that $ON = 8$, $SR=20$, $NM = 10$, and $RQ=x$.

Step2: Set up the proportion

From the SAS similarity condition, we set up the proportion: $\frac{ON}{SR}=\frac{NM}{RQ}$. Substituting the known values, we get $\frac{8}{20}=\frac{10}{x}$.

Step3: Solve for x

Cross - multiply the proportion: $8\times x=20\times10$. So $8x = 200$. Then, divide both sides by 8: $x=\frac{200}{8}=25$.

Answer:

25