In Figure 3, PQ || CD and PR || CB. Prove that

Question:

In Figure $3, P Q \| C D$ and $P R \| C B$. Prove that $\frac{A Q}{Q D}=\frac{A R}{R B}$.

Solution:

Given that:

$P Q \| C D$ and $P R \| C B$, then we to prove that $\frac{A Q}{Q D}=\frac{A R}{R B}$

The following diagram is given

We can easily see that, in the above figure  are similar triangles, and also the are similar triangles.

Now, we have the following properties of similar triangles,

$\frac{A Q}{Q D}=\frac{A P}{P C}$     ................(1)

$\frac{A R}{R B}=\frac{A P}{P C}$      ................(2)

From equation (1) and Equation (2), we get

$\frac{A Q}{Q D}=\frac{A R}{R B}$

Hence proved.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now