Question

A B C D is a
trapezium
AB//CD, AE=ED, EF// AB // CD
Prove- 1) F is midpoint of BC
2)EF =½(AB+CD)​

Answer 1

Step-by-step explanation:

1.AE=ED

BF=FC

F is midpoint of BC

Answer 2

Answer:

we can solve it by mid point theorem

Step-by-step explanation:

AE=ED is given. That means E is the midpoint of AD.

Construction: Join AC.

Proof: In ∆ADC,

AE=ED

EO||DC

:. By converse of mid point theorem, O is the midpoint of AC.

Also EO=1/2 DC...........(1)

In ∆BAC,

AO=OC

OF||AB

:. By converse of mid point theorem, F is the midpoint of BC [(i) is proved]

Also OF=1/2 AB.............(2)

Adding (1) and (2), we get

EO+OF=1/2 DC+ 1/2 AB

EF=1/2(AB+DC) [(ii) is proved]

#together_we_go_far❤️