Given: abcd is a parellelogram.
prove: ab=cd and bc=da

Step-by-step explanation:

We have given a parallelogram ABCD.

For a parallelogram,

Opposite pair of sides are parallel to each other.

i.e AD is parallel to BC and AB is parallel to CD.

From the attached figure,

∡1 = ∡4  and  ∡2 = ∡3    {If two parallel lines cut by a transversal line then alternate interior angles are congruent }

Next, AC ≅ AC  {Reflexive identity}

hence, ΔABC ≅ ΔCDA   , By Angle-Side-Angle(ASA) congruent property of triangle.

Therefore, AB = CD  and AD = BC   {Proved}

Parallelograms have a pair of parallel sides and angles.

The statements of proof and the reasons are:

From the question, we have:

ABCD is a parallelogram.

So, the reason for the above statement would be "Given"

From the figure, we have:

AD is parallel to BC and AB is parallel to CD.

This means that:

The angles at opposite vertices are congruent.

So, we have:

The reason for the above statement would be "Definition of alternate interior angles"

Also, we can see that:

Lines AC and BD are diagonals, and they meet at a point

The reason for the above statement would be "Unique line postulate"

The above statement means that:

The reason for the above statement would be "Definition of parallelogram"

Hence, ABCD has been proven to be a parallelogram.

Read more about proofs of parallelograms at:

link

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm