Median divides triangle into two triangles of equal area
Question 3 - Median divides triangle into two triangles of equal area - Areas of Parallelograms and Triangles
Last updated at April 16, 2024 by Teachoo
Since rectangle, square, rhombus are all parallelograms.
We can also say that
Diagonals of a rectangle divide it into 4 triangles of equal area
OR
Diagonals of a square divide it into 4 triangles of equal area
OR
Diagonals of a rhombus divide it into 4 triangles of equal area
Transcript
Question 3
Show that the diagonals of a parallelogram divide it into four triangles of equal area.
Given: A parallelogram ABCD
With diagonals AC & BD
To prove: ar (∆AOB) = ar (∆BOC) = ar (∆COD) = ar (∆AOD)
Proof : ABCD is a parallelogram
Diagonals of a parallelogram bisect each other
∴ O is the mid-point of BD, i.e., OB = OD
& O is the mid-point of AC, i.e., OA = OC
In ∆ ABC,
Since OA = OC
∴ BO is the median of ∆ ABC
⇒ ar(∆ AOB) = ar(∆ BOC)
In ∆ ADC,
Since OA = OC
∴ DO is the median of ∆ ADC
⇒ ar(∆ AOD) = ar(∆ COD)
Similarly,
In ∆ABD,
Since OB = OD
∴ AO is the median of ∆ ABD
⇒ ar(∆ AOB) = ar(∆ AOD)
From (3) , (4) & (5)
ar (∆AOB) = ar (∆BOC) = ar (∆COD) = ar (∆AOD)
Hence proved
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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