Question

in a triangle ABC,AB =8cm ,BC=7cm ,AC=6cm
D,E and F are midpoints of AB,BCand CA respectively
find the lengths of the sides of triangle DEF

Answer 1

in a triangle ABC,AB =8cm ,BC=7cm ,AC=6cm

in a triangle ABC,AB =8cm ,BC=7cm ,AC=6cmD,E and F are midpoints of AB,BCand CA respectively .

$\underline { \pink { By \:Midpoint \: Theorem \:of \: Triangle : }}$

The line segment joining the mid-points of two sides of a triangle is parallel to the third side and also half of it .

$i ) DE = \frac{1}{2} \times AC \\ = \frac{1}{2} \times 6 \\ = 3 \:cm$

$ii ) DF = \frac{1}{2} \times BC \\ = \frac{1}{2} \times 7 \\ = 3.5 \:cm$

$iii )EF = \frac{1}{2} \times AB \\ = \frac{1}{2} \times 8 \\ = 4 \:cm$

Therefore.,

$\green { DE = 3 \:cm , \:DF = 3.5 \:cm ,\:EF = 4 \:cm }$

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Answer 2

Given :   triangle ABC, AB = 8 cm, BC = 7 cm and AC = 6 cm.

D, E and F are the midpoints of AB, BC and CA respectively.

To Find : the lengths of the sides of triangle DEF.​

Solution:

line joining the mid-point of two sides of a triangle is equal to half the length of the third side

D, E  are the midpoints of AB, BC  

hence DE = AC/2   =  6/2  = 3 cm

F, E  are the midpoints of CA, BC  

hence EF = AB/2   =  8/2  =4 cm

D  and F are the midpoints of AB and CA

=> DF  = BC/2  = 7/2  = 3.5 cm

lengths of the sides of triangle DEF.​

DE = 3 cm , EF  = 4 cm , DF  = 3.5 cm

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