Question

In the figure, seg AB and seg CD intersect at the point O. OA=15cm, OB=12cm, OC=10cm, OD=8cm. State whether ΔAOC and ΔBOD are similar or not. If so by which test?

Answer 1

please refer the attachment

Answer 2

Answer:

ΔAOC and ΔBOD are similar by SAS similarity

Step-by-step explanation:

Here, segment AB and segment CD intersect at the point O. OA=15cm, OB=12cm, OC=10cm, OD=8cm.

We have to check whether ΔAOC and ΔBOD are similar or not.

In ΔAOC and ΔBOD, the sides are proportional

i.e $\frac{AO}{OB}=\frac{CO}{OD}=\frac{5}{4}$

and ∠AOC=∠BOD  (vertically opposite angles)

Hence, By SAS similarity theorem,

ΔAOC and ΔBOD are similar