Question

c)
In TriangleABC, D is the midpoint of AB, E is the midpoint of AC. Calculate
ODE if BC =8cm
(inAngle ADE if Angle DBC = 1250​

Answer 1

Given:  A quadrilateral ABCD and BD is a diagonal.

To prove:   ABCD is a parallelogram.

Construction:   Draw AM ⊥ DC and CL ⊥ AB   (extend DC and AB). Join AC, the other diagonal of ABCD.

Proof: ar(quad. ABCD) = ar(∆ABD) + ar(​∆DCB)

                                     = 2 ar(​∆ABD)                    [∵ ar​(∆ABD) = ar(​∆DCB)]

∴ ar(​∆ABD) = 12ar(quad. ABCD)                 ...(i)

Again, ar(quad. ABCD) = ar(∆ABC) + ar(​∆CDA)

                                   = 2 ar(​∆ ABC)                    [∵ ar​(∆ABC) = ar(​∆CDA)]

∴ ar(​∆ABC) = 12ar(quad. ABCD)                ...(ii)

From (i) and (ii), we have:

ar(​∆ABD) = ar(​∆ABC) = 12 AB ⨯ BD = 12 AB ⨯ CL

⇒ CL = BD

⇒ DC |​​| AB

Similarly, AD |​​| BC.

Hence, ABCD is a paralleogram.

∴ ar(​|​| gm ABCD) = base ​⨯ height = 5 ​⨯ 7 = 35 cm2

@krishhhhhhna