Question

In the figure seg ab and seg cd intersect at point O oa 15cm ob 12 cm oc 10cm od8cm state weather AOC AND BOD ARE SIMILAR OR NOT IF SO BY WHICH TEST.

Answer 1

Answer: Triangle AOC and BOD are similar.

Step-by-step explanation:

Given: Line segments AB and CD intersect at O.

AO = 15, OC = 10, OB = 12 and OD = 8

To Prove: $\triangle AOC\sim \triangle BOD$

Proof:

Since, $\frac{AO}{BO} = \frac{15}{12} = \frac{5}{4}$

Also,  $\frac{OC}{OD} = \frac{10}{8} = \frac{5}{4}$

Thus,  $\frac{AO}{BO} = \frac{OC}{OD}$

Also, $\angle COA\cong \angle BOD$ ( vertically opposite angles)

Therefore, by SAS similarity postulate,

$\triangle AOC\sim \triangle BOD$

Hence, proved.