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State true or false.

In the given figure, $A B C$ is a triangle in which $A B = A C$ and $D$ is a point on $A B$ . Through $D$ , a line $D E$ is drawn parallel to $B C$ and meeting $A C$ at $E$ . Then $A D ≠ A E$ .

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True

False

answer is B.

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Detailed Solution

It is given that

A B = A C

D

is a point on

A B

D E

is drawn parallel to

B C

and meeting

A C

E

From the above figure,

A B = A C

and

D E ∥ B C

.
By basic proportionality theorem,

A D D B = A E E C

and

D B A D = E C A E

……(1)
Analyze equation (1) and add 1 on both sides.

D B A D + 1 = E C A E + 1

By simplification,

D E + A D A D = E C + A E A E

A B A D = A C A E

But

A B = A C

A B A D = A C A E

A D = A E

But the statement given is

A D ≠ A E

.
Hence the given statement is false.
Hence the correct statement is for a triangle ABC, when a line DE is parallel to BC and meeting AC at E, thn AD = AE.
Therefore option 2 is correct.

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