Question

D E and F are respectively the midpoints of sides ab bc and ac of triangle ABC prove that ΔABC is similar to ΔDEF PLS ANSWER IT IS VERY URGENT?​

Answer 1

Step-by-step explanation:

We know that line joining the mid-points of two sides of a triangle is parallel to the 3rd side.

D and F are mid-points of AB and AC respectively

Therefore, DF is parallel to BC

So, DF parallel to BE also ----------(1)

Similarly,

E and F are mid-points of BC and AC respectively,

EF is parallel to AB

Hence EF is also parallel to DB-------------(2)

From 1 & 2,

DF parallel to BE and EF is also parallel to DB

Therefore, opposite sides of a quadrilateral is parallel

DBEF is a parallelogram.

We know that, in a parallelogram opposite angles are equal.

Hence, Angle DFE = Angle ABC--------3

Similarly, We can prove that DECF is a parallelogram

In a parallelogram, opposite angles are equal

Therefore, Angle EDF = Angle ACB-----------4

Now in Triangle EDF and Triangle ABC,

Angle DFE = Angle ABC (from 3)

Angle EDF = Angle ACB (from 4)

By using AA similarity criterion Triangle DEF ~ Triangle ABC

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