Question

If $\overleftrightarrow{AD}||\overleftrightarrow{BC},$ then area $\left(\Delta ABC\right)$ = area $\left(\Delta BEC\right)$. = area $\left(\Delta DBC\right)$. Say true or false.

• A. True
• B. False

Answer 1

The correct option is A

True

If $\overleftrightarrow{AD}||\overleftrightarrow{BC},$ then area $\left(\Delta ABC\right)$ = area $\left(\Delta BEC\right)$ = area $\left(\Delta DBC\right)$. This is because base lengths of all the triangles are same and heights are also equal since they lie between same parallel lines. This is generally stated as

Two or more triangles having a common base and lying between same parallel lines will have equal areas.

Actually, any two triangles, even with equal base, if not common and between same parallels will also have equal area.