Question

In this figure, if PQ ll BC and PR ll CD, prove that QB/AQ = DR/AR.​

Answer 1

Step-by-step explanation:

Given that:if PQ ll BC and PR ll CD.

To prove: prove that QB/AQ = DR/AR.

Solution:

In ∆ABC

Since PQ ll BC

$\bold{\frac{QB}{AQ}=\frac{PC}{AP}}\:\:\:...eq1\:\:[By\:BPT]$

In ∆ACD

Since PR ll CD

$\bold{\frac{PC}{AP}=\frac{DR}{AR}}\:\:\:...eq2\:\:[By\:BPT]$

From eq1 and eq2

$\bold{\frac{QB}{AQ}=\frac{DR}{AR}}\:\:\:$

Hope it helps you.

Answer 2

Step by step explanation:

In △ABC, we have

PQ∣∣BC

Therefore, by basic proportionality theorem, we have

AB

AA= AC/AP ........(i)

In △ACD, we have

PR∣∣CD

Therefore, by basic proportionality theorem, we have

AC

AP

=

AD

AR

From (i) and (ii), we obtain that

AB

AQ

=

AD

AR

or

AD

AR

=

AB

AQ

[Hence proved]

⇒

AQ

AB

=

AR

AD

⇒

AQ

AQ+QB

=

AR

AR+RD

⇒ 1+

AQ

QB

=1+

AR

RD

⇒

AQ

QB

=