Question

4. Suppose it is known that DE=DF. Then, is traingle ABC isosceles? Why or why not​

Answer 1

Answer:

yes

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.