#
$14.Intheadjoiningfigure,ABCDisatrapaziumwithADandBCasparallelsidesand\angle BAD={90}^{o}\phantom{\rule{0ex}{0ex}}BDandACcutatE.ProvethatthetriangleABEisequalinareatothetriangleCED$

Please find below the solution to the asked query:

13 ) From given diagram we know : BC | | DE

So,

Height of $\u2206$ BCD = Height of $\u2206$ BCE =

*h*( As both triangles lies between same parallel lines " DE | |BC " by taking base ' BC ' )

We know : Area of triangle = $\frac{1}{2}$ $\times $ Base $\times $ Height , So

Area of $\u2206$ BCD = $\frac{1}{2}$ $\times $ BC $\times $

*h*--- ( 1 )

And

Area of $\u2206$ BCE = $\frac{1}{2}$ $\times $ BC $\times $

*h*--- ( 2 )

From equation 1 and 2 we get :

Area of $\u2206$ BCD = Area of $\u2206$ BCE

Now we subtract ' Area of $\u2206$ BOC ' on both hand side we get :

Area of $\u2206$ BCD - Area of $\u2206$ BOC = Area of $\u2206$ BCE - Area of $\u2206$ BOC

We know from Third Axiom of Euclid " If equals be subtracted from equals, the remainders are equal. " So

**Area of $\u2206$ BOD = Area of $\u2206$ COE ( Hence proved )**

Hope this information will clear your doubts about topic.

For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.

Regards

**
**