In the figure, $s e g A B$ and $seg C D$ intersect at the point $O . O A = 15 c m . O B = 12 c m . O C = 10 c m O D = 8 c m . State whether △ A O C and △ B O D$ similar or not. If so, by which test?

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Solution

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, AO/BO = 5/4

And, OC/OD= 5/4

Thus, OA/OB= OC/OD

Also, ( vertically opposite angles)

Therefore, by SAS postulate of similarity,

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s e g A B ∥ s e g C D

A C

B D

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\frac{A (△ A O B)}{A (△ A B D)} =

seg A B ≅ seg C B and seg A D ≅ seg C D .

△ A B D ≅ △ C B D

In the fig. $s e g A B ∥ s e g C D$ and $s e g A B ≅ s e g C D$ prove that $s e g A C$ and $s e g B D$ bisect each other at point $P$ .

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