Question

in fig seg AB and seg CD intersect at the point o . OA=15cm OB=12cm OC=10cm OD=8cm .State whether triangle AOC and triangle BOD are similar or not .If so by which test

Answer 1

Answer: Yes, triangles AOC and BOD are similar.

Step-by-step explanation:

Here, segment AB and segment CD intersect at the point O.

By joining point A and  B with points C and D respectively. ( construction)

We get, two triangles, AOC and BOD.

Given: OA = 15 cm  OC = 10 cm, OD = 8 cm and OB = 12 cm,

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

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

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

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

Therefore, by SAS postulate of similarity,

$\triangle AOC\sim \triangle BOD$