Respuesta :

Answer:


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}


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MrRoyal

Parallelograms have a pair of parallel sides and angles.

The statements of proof and the reasons are:

  • ABCD is a parallelogram ---- Given
  • [tex]\mathbf{\angle A \cong\ \angle C \ and\ \angle B \cong \angle D}[/tex] ----- Definition of alternate interior angles
  • Lines AC and BD are diagonals ---- Unique line postulate
  • [tex]\mathbf{AB \cong\ CD \ and\ BC \cong DA}[/tex] ------ Definition of parallelogram

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:

[tex]\mathbf{\angle A \cong\ \angle C \ and\ \angle B \cong \angle D}[/tex]

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:

[tex]\mathbf{AB \cong\ CD \ and\ BC \cong DA}[/tex]

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:

https://brainly.com/question/4626921

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