PYQ - Prove the statement — task. Maths TNSB Mentoring, Class 10 Crash course.

In figure \(DE || BC\) and \(CD || EF\), prove that \(AD^2 = AB \times AF\).

Proof:

Consider a \(\Delta ADC\), we have \(CD || EF\).

By basic proportionality theorem:

- - - - - - - - (I)

Now, consider a \(\Delta ABC\), we have \(DE || BC\).

By basic proportionality theorem:

- - - - - - - - (II)

From (I) and (II), we get

Taking reciprocal on both sides.

Add \(1\) on both sides of the equation.

Hence it is proved.

Answer variants:

AD \times AD = AB \times A F

\frac{F D + A F}{A F} = \frac{DB + AD}{AD}

\frac{A F}{F D} = \frac{AD}{DB}

\frac{F D}{A F} + 1 = \frac{DB}{AD} + 1

\frac{A F}{F D} = \frac{AE}{EC}

\frac{AD}{A F} = \frac{AB}{AD}

\frac{F D}{A F} = \frac{DB}{AD}

{AD}^{2} = AB \times A F

\(\frac{AD}{DB} = \frac{AE}{EC}\)

Did you find an error?

7. PYQ - Prove the statement