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State true or false.

If in the given figure, ABCD is a cyclic quadrilateral whose sides AB and DC are produced to meet in E, then $△ E B C$ is not similar to $△ E D A$ .

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True

False

answer is B.

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Detailed Solution

It is given that ABCD is a cyclic quadrilateral whose sides AB and DC are produced to meet in E.
Question Image

We have to check if

△ E B C

is not similar to

△ E D A

.
Considering the

△ E B C

△ E D A

.
Since the exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. So,

∠ E B C = ∠ C D A

∠ E B C = ∠ E D A ..... (1)

And,

∠ E C B = ∠ B A D

∠ E C B = ∠ E A D ..... (2)

Since both angle

∠ B E C & ∠ D E A

represent the same angle.
So,

∠ B E C = ∠ D E A ...... (3)

Using a similar test for triangle

△ E B C

△ E D A

.
From (1), (2), and (3), it is clear that two angles of one triangle

△ E B C

are respectively equal to two angles of another triangle

△ E D A

.
Hence,

△ E B C

is not similar to

△ E D A

.
Thus, the statement is false.
Therefore, option 2 is correct.

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