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State true or false.

If P is a point on the median AD of a $Δ A B C$ , then area ( $Δ A B P$ ) = area ( $Δ A C P$ ).

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True

False

answer is A.

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Detailed Solution

Given in

Δ ABC

, P is a point on the median AD.
Since, AD is the median.
Thus, BD = DC.
Consider the height of

Δ ABC

be h,

area Δ ABD = area Δ ACD 12 × h × BD = 12 × h × CD

Consider H to be the height of ∆BPD and of ∆PDC.

area Δ BPD = area Δ CPD 12 × H × BD = 12 × H × CD

From the figure,

area Δ ABD = area Δ ABP + area Δ BPD

,
And,

area Δ ACD = area Δ ACP + area Δ PDC

.
From the above results, thus,

area Δ ABP = area Δ ACP

.
Hence the given statement is true.
Option 1 is the correct choice.

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