Question

in abc e and f are midpoints of sides ab and ac respectively then prove that (1) EF || BC AND EF = 1/2 BC

Answer 1

EH II BC and EF = 1/2BC (by mid point theoram).

Answer 2

Answer:

Cons:- draw a line parallel to AB from point C and extend DE line to meet point F.

Step-by-step explanation:

• Proof:- in  triangle AEF and triangle CEF

                    ∠EAF=∠FCD                            (∵alternate angle)

                   AF=FC                                       (∵F is mid point)

                  ∠AFE=∠CFD                              (∵vertically opposite angle)

                  therefore by ASA congruency rule

                  AEF ≅CFD

                  So EF=DF and AE= DC (∵CPCT)

                  BE=AE=DC

                  BCDE is a parallelogram.

                  so that EF║ BC

Hence proved.

• As we proved earlier both triangle are similar

                    let AE=x

                   then AB=2x

                  ⇒AE/AB=EF/BC

                 ⇒  x/2x=EF/BC

                 ⇒  1/2=EF/BC

                  ⇒EF=1/2BC

Hence proved.