Question

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Complete the following proof.

Prove: The opposite sides of a parallelogram are equal.

Answer 1

Explanation:

Prove: The opposite sides of parallelogram are equal.

Proof: The given points are A(0,0) and D(c,d) are:

Using distance formula, we have

`AD=√((c-0)^2+(d-0)^2)=√(c^2+d^2)`

The given points are B(b,0) and C(b+c,d) are:

Using distance formula, we have

`BC=√((b+c-b)^2+(d-0)^2)=√(c^2+d^2)`

The given points are A(0,0) and B(b,0) are:

Using distance formula, we have

`AB=√((b-0)^2+(0-0)^2)=√(b^2+0^2)=√(b^2)`

The given points are C(b+c,d) and D(c,d) are:

Using distance formula, we have

`CD=√((c-(b+c))^2+(d-d)^2)=√(b^2+0^2)=√(b^2)`

Hence, AD=BC and AB=CD, therefore opposite sides of parallelogram are equal.

Answer 2

The first thing we should do is find AD:
AD=root((c-0)^2 + (d-0)^2)=root((c)^2 + (d)^2)
We now look for the value of BC:
BC=root(((b+c) - b)^2+(d-0)^2)=root((c)^2+(d)^2)
Then, we look for AB:
AB=root((b-0)^2 + (0-0)^2)=root((b)^2 + (0)^2)=root((b)^2)
Finally, we look for the value of CD: CD=root((c-(b+c))^2 + (d-d)^2)
CD=root((b)^2 + (0)^2)
CD=root((b)^2)