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


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


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.

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