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Complete the following proof.

Prove: The opposite sides of a parallelogram are equal.

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)

Answer Link

boffeemadrid boffeemadrid · Answer 2 · 2019-06-04T07:30:46+02:00

Answer:

Step-by-step 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

[tex]AD=\sqrt{(c-0)^2+(d-0)^2}=\sqrt{c^2+d^2}[/tex]

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

Using distance formula, we have

[tex]BC=\sqrt{(b+c-b)^2+(d-0)^2}=\sqrt{c^2+d^2}[/tex]

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

Using distance formula, we have

[tex]AB=\sqrt{(b-0)^2+(0-0)^2}=\sqrt{b^2+0^2}=\sqrt{b^2}[/tex]

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

Using distance formula, we have

[tex]CD=\sqrt{(c-(b+c))^2+(d-d)^2}=\sqrt{b^2+0^2}=\sqrt{b^2}[/tex]

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