Question

if two triangles have a common vertex and their basis lie on the same line then their areas are proportional to the lengths of their bases??

Answer 1

The areas of the two triangles are proportional to the lengths of their bases.

Step-by-step explanation:

See the attached diagram.

We have two triangles Δ ABC and Δ ADE having the same vertex A and their bases lie on the same line BE.

The area of the triangle Δ ABC will be equal to

X = $\frac{1}{2} \times (\textrm {Height})\times (\textrm {Base})$

X =  $\frac{1}{2}\times AH \times BC$

Again, the area of the triangle Δ ADE will be

Y = $\frac{1}{2} \times AH \times DE$

Hence, $\frac{X}{Y} = \frac{BC}{DE}$

Hence, the areas of the two triangles are proportional to the lengths of their bases. (Answer)