Q. 164.3( 12 Votes )
If D, E, F are the mid-points of sides BC, CA and AB respectively of A ABC, then the ratio of the areas of triangles DEF and ABC is
A. 1 :4
B. 1 : 2
C. 2 : 3
D. 4 : 5
Given D, E and F are the mid-points of sides BC, CA and AB respectively of ΔABC.
Then DE || AB, DE || FA … (1)
And DF || CA, DF || AE … (2)
From (1) and (2), we get AFDE is a parallelogram.
Similarly, BDEF is a parallelogram.
In ΔADE and ΔABC,
⇒ ∠FDE = ∠A [Opposite angles of ||gm AFDE]
⇒ ∠DEF = ∠B [Opposite angles of ||gm BDEF]
∴ By AA similarity criterion, ΔABC ~ ΔDEF.
We know that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
∴ ar (ΔDEF): ar (ΔABC) = 1: 4
Rate this question :
, ar () = 9 cm2, ar () = 16 cm2. If BC = 2.1 cm, then the measure of EF isRD Sharma - Mathematics
. such that ar () = 4 ar (). If BC =12 cm, then QR =RD Sharma - Mathematics
If and are two triangles such that , then Area (): Area () =RD Sharma - Mathematics
The areas of two similar triangles are in respectively 9 cm2 and 16 cm2. The ratio of their corresponding sides isRD Sharma - Mathematics
The areas of two similar triangles and are 144 cm2 and 81 cm2 respectively. If the longest side of larger A ABC be 36 cm, then. the longest side of the smaller triangle isRD Sharma - Mathematics
In Fig. 4.236, and AP : PB = 1 : 2. Find [CBSE 2008]
RD Sharma - Mathematics
If and are two triangles such that , then write Area (): Area ().RD Sharma - Mathematics