If P is any point on the median A D of a A B C- then ar - ABPar - ACP-

Given: nbsp;P nbsp;is any point on the median nbsp;AD nbsp;of a Delta;ABC We know, median of a triangle divides it into two triangles of equal area. ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Tests for Congruency of Triangles

If P is any p...

Question

If P is any point on the median AD of a ΔABC, then $\frac{ar (∆ A B P)}{ar (∆ A C P)}$ = _________.

Open in App

Solution

Given: P is any point on the median AD of a ΔABC

We know, median of a triangle divides it into two triangles of equal area.

Therefore, ar (ΔADB) = ar (ΔADC) ...(1)
Also, ar (ΔPDB) = ar (ΔPDC) ...(2)

Subtracting (2) from (1), we get
ar (ΔADB) − ar (ΔPDB) = ar (ΔADC) − ar (ΔPDC)
⇒ ar (ΔABP) = ar (ΔACP)
⇒ $\frac{ar (∆ A B P)}{ar (∆ A C P)}$ = 1

Hence, $\frac{ar (∆ A B P)}{ar (∆ A C P)}$ = 1.

Suggest Corrections

Similar questions

Q. In

E

is any point on median

A D

of a

Δ

A B C

. Show that ar

(A B E) = ar (A C E)

Δ

ABC and

Δ

DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that

Δ

ABP

≅

Δ

ACP.

Q. In

Δ

ABC, AD is the median and AB = AC. Then by which similarity criterion are

Δ

ADB and

Δ

ADC similar?

Q. If AD, BE and CF are the medians of

Δ

ABC, then which one of the following statements is correct?

Q. In given

Δ

ABC, AD and BE are medians of triangle which intersect each other at point G. If area of

Δ

BDG is

1

c m^{2}

, then what is the area of DCEG?

Join BYJU'S Learning Program

If P is any point on the median AD of a ΔABC, then ar ∆ABPar ∆ACP= _________.

If P is any point on the median AD of a ΔABC, then $\frac{ar (∆ A B P)}{ar (∆ A C P)}$ = _________.