Question

In figure AE=DF,E is the midpoint of AB and F us the mid point of DC. using an eucleids axiom show that AB=DC

Answer 1

AE = DF
2AE = 2DF
( using axiom. double of equals are also equal)
AB = CD
HENCE PROVED

IF U WANT TO SHOW HOW 2AE = AB
USE
E is the midpoint of AB
AE = EB
adding AE on both sides
AE + AE = BE + AE
2AE = AB

Answer 2

AB = CD

GIVEN

AE = DF

E is the midpoint of AB

F is the midpoint of DC

TO PROVE

AB = DC (Using Euclid's axiom)

SOLUTION

We can simply solve the above problem as follows;

It is given that,

E is the midpoint of AB

This means that,

AE = EB

AB = AE + EB (Equation 1)

Similarly,

F is the midpoint of DC

Therefore,

CF = DF

DC = CF + DF (Equation 2)

According to the question,

AE = DF

Multiplying the whole equation by 2

2AE = 2DF.

According to Euclid's axiom, The double of equals is also equal.

We can write the above equation as;

AE + EB = CF + DF

From equation 1 and 2

AB = CD

AB = CD Hence, proved.

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