Maths / Areas Of Parallelograms And Triangles / Median and Altitude of Triangle

QUESTION

In triangle ABC, D and E are points on BC such BD = DE = EC. Show that ar($\dpi{120} \fn_jvn \large \Delta$ABD) = ar($\dpi{120} \fn_jvn \large \Delta$ADE) = ar($\dpi{120} \fn_jvn \large \Delta$AEC).

EXPLANATION
Explain TypeExplanation Content
Text

BD - DE

$\therefore$  AS is the median of $\Delta$ABE.

$\therefore$  ar ($\Delta$ABD) = ar($\Delta$AED)        [By throrem]

DE = EC

$\therefore$   AE is the median of $\Delta$ADC.

$\therefore$  ar($\Delta$ADE ) = ar ($\Delta$ACE)       [By theorem]

$\therefore$  ar ($\Delta$ABD) = ar(ADE) = ar($\Delta$ACE)

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