Question

in the given figure, AD is the median of triangle ABC and E is the midpoint of AD. prove that ar(triangle BDE)=ar(triangle ABC)

Answer 1

Step-by-step explanation:

Because, E is the mid point on median AD. so if we draw a line from B to E so, BE is a median.

Because AD and BE are median then,,

DB = DC and EA = DE

In triangle ABC, AD is a median

as we know a median divides a triangle into 2 equal halves,

ar.(ABC) = ar.(CAD) or

ar.(ABD) = 1/2 ar.(ABC)           ____(1)

similarly,

ar.(BEA) = ar.(BED)  or

ar.(1/2 ABD) = ar.(BED)           _____(2)

Substituting value of (1) in (2)

ar.(1/2 * 1/2 ABC ) = ar.(BED)

= ar.(1/4 ABC) = ar.(BED)

                                        HENCE PROVED

                   HOPE IT HELPS !!!!!!!!!!!!!!!!!!!!!!!!!!!!!1