What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?

16, 20, 25, 50

Solution:

In △ONM and △SRQ

∠ONM is similar to ∠SRQ

From the figure

NM = 10

SR = 20

NO = 8

QR = x

Using the SAS similarity theorem we have to find the value of x

SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Both the triangles are similar by SAS if

NO/NM = SR/QR

Now substitute the values

8/10 = 20/x

By cross multiplication

8x = 200

By dividing both sides by 8

x = 25

Therefore, the value of x is 25.

---

What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?
16, 20, 25, 50

Summary:

The value of x which will make △ONM similar to △SRQ by the SAS similarity theorem is 25.