Question

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. The diagram is not drawn to scale?

Answer 1

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

Explanation:

Givn : OK = 3, OJ = 30, KN = 1, JM = 3#

`ON = OK + KN = 3 + 1 = 4`

`OM = OJ + JM = 30 + 10 = 40`

In triangles OKJ & ONM,

`(OK) / (OJ) = 3 / 30 = 1/10`

`(ON) / (OM) = 4 / 40 = 1/10`

Angle O is common in both the triangles.

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

That means `(KJ) / (NM) = 1/10` or the two sides are parallel.

Hence `hatK = hatN, hatJ = hatM` corresponding angles.

That means the three angles of triangle OKJ are equal to the corresponding three angles of triangle ONM.

Hence the to triangles are similar.