Q. 243.7( 3 Votes )

# In Fig. 17.29, suppose it is known that *DE* = *DF*. Then, is Δ*ABC* isosceles? Why or why not?

Answer :

In parallelogram BDEF

BD = EF and BF = DE ……..(i) [In a parallelogram opposite sides are equal]

In parallelogram DCEF

DC = EF and DF = CE ……..(ii) [In a parallelogram opposite sides are equal]

In parallelogram AFDE

AF = DE and DF = AE ……..(ii) [In a parallelogram opposite sides are equal]

Therefore DE = AF =BF ……..(iv)

Similarly: DF = CE = AE …….(v)

But, DE = DF ……given

From equations (iv) and (v), we get

AF + BF = AE + EC

AB = AC

Therefore ΔABC is an isosceles triangle.

Rate this question :

The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.

RD Sharma - MathematicsThe angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is

NCERT - Mathematics Exemplar