Question

From the given figure match the following.

• A. $\frac{AB}{BC}$
• B. $\frac{AB}{AC}$
• C. $\frac{BC}{AC}$

Answer 1

Areas of triangles with the same bases along the same straight line are in the ratio of their bases.

Here in the figure the triangles $△ABD,△BCD\text{and}△ACD$ have the same vertex D and bases along the same straight line AC, therefore they have the same height. In such cases the areas of the triangles are in the ratio of their bases.

$\Rightarrow \frac{\text{Area of triangle}△ABD}{\text{Area of triangle}△BCD}=\frac{AB}{BC}$

$\Rightarrow \frac{\text{Area of triangle}△ABD}{\text{Area of triangle}△ACD}=\frac{AB}{AC}$

$\Rightarrow \frac{\text{Area of triangle}△BCD}{\text{Area of triangle}△ACD}=\frac{BC}{AC}$