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State true or false.

In the adjoining figure, $X$ and $Y$ are respectively two points on equal sides $A B$ and $A C$ of $Δ A B C$ such that $A X = A Y$ . Then $C X = B Y$ .

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True

False

answer is A.

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Detailed Solution

It is given that

X

and

Y

are respectively two points on equal sides

A B

and

A C

such that

A X = A Y

We have to show that

C X = B Y

.
Consider

Δ C X A

and

Δ B Y A .

A X = A Y

∠ X A C = ∠ Y A B

…(Common angle)

A C = A B

Therefore, by SAS congruence criteria,

Δ C X A ≅ Δ B Y A .

By Congruent Parts of Congruent Triangles,

C X = B Y

.
In the adjoining figure,

X

and

Y

are respectively two points on equal sides

A B

and

A C

Δ A B C

such that

A X = A Y

. Then

C X = B Y

.
Hence the statement is true.
Hence option 1 is correct.

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