Question

In given fig.PQ||RS.prove ∆POQ~∆ROS​

Answer 1

In the given figure, PQ || RS.

So, we can conclude that :-

∠P = ∠S (Alternate interior angles are equal)

∠Q = ∠R (Alternate interior angles are equal)

also, ∠POQ = ∠ROS (vertically opposite angles are equal)

Now, since all three angles are equal, we can conclude that ΔPOQ ~ ΔROS.

"Two triangles are similar if at least two of the interior angles of them are equal, or the ratio of their corresponding sides are equal"

NOTE :- While writing similarity, put equal angles in correct manner. Here, for example, ∠P = ∠R, ∠Q = ∠S, ∠POQ = ∠ROS. So, the similarity of these two triangles would be written as ΔPOQ ~ ΔROS and not ΔPOQ ~ ΔSOR or ΔQOP ~ ΔROS and so on.

Answer 2

Answer:

pq is parallel to rs thus

<qps=<psr(alt int angles)

<pqr=<psr("         "        "    ")

<poq+<sor(vertically opposite angle)

thus by aaa criteria ∆POQ~∆ROS

Step-by-step explanation: