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First draw a parallelogram. I cannot draw one here so I will have to describe the picture and you should draw it. Let ABCD be a parallelogram. I put A on the bottom left, then B on the bottom right, C on the top right and D on the top left. Of course the arguments must apply to an arbitrary parallelogram, but just so you can follow the proof, that is my drawing. Now draw a segment from A to C. It is a diagonal. AB is parallel to CD and AD is parallel to BD because a parallelogram is a quadrilateral with both pair of opposite sides parallel. Now ABC and CDA both form triangles. Let angles 1 and 4 be the angles created by the diagonal and angle BCD of the parallelogram. Angle 1 is above and angle 4 is below. Similarly, let angles 3 and 2 be created by the intersection of the diagonal and angle DAB or the original parallelogram. Now angles 1 and 2 are congruent as are 3 and 4 because if two parallel lines are cut by a transversal, the alternate interior angles are congruent. Next using the reflexive property AC is congruent to itself. Now triangle ABC is congruent to triangle CDA by Angle Side Angle (SAS). This means that AB is congruent to CD and BC is congruent to AD by corresponding parts of congruent triangles are congruent (CPCTC). So we are done!

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Q: Proving that a parallelogram has equal pair of sides?
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Related questions

What are the differences between a rhombus trapezoid and a parrallelogram?

A trapezium has only one pair of parallel sides. A parallelogram has two pair of parallel sides. A rhombus is an equilateral parallelogram - that is, a parallelogram with equal sides.


Does a parallelogram have at least one pair of equal sides?

ya


What is a quadrangle that has two pair of equal sides and not a parallelogram?

Thats impossible and its a parallelogram either way


When can a trapezoid be a parallelogram?

It cannot. A trapezium is a quadrilateral that has one pair of parallel but unequal sides and another pair of non-parallel sides. A parallelogram has two pairs of parallel and equal sides.


What is a quadrangle that has 2 pair of equal sides but is NOT a parallelogram?

It could be an arrowhead.


Why is a parallelogram not a trapezoid?

Both a parallelogram and the trapezoid are quadrilaterals (meaning they both have 4 sides). However, in a parallelogram, both pairs of opposite sides are parallel and equal. But in a trapezoid, only one pair of sides are parallel, and the other pair are not).


What is a figure that has 1 pair of equal angles and has 2 pairs of equal adjacent sides?

a parallelogram


Are all pairs of opposite sides equal in all of the parallelograms?

Yes. If a pair of opposite sides are not equal, then you don't have a parallelogram.


Is a trapezoid a parallelogram with 4 equal sides but no right angles?

No. A trapezoid is a 4-sided polygon with one pair of parallel sides. A parallelogram with 4 equal sides is a rhombus. (A parallelogram with 4 equal sides and 4 right angles is a square, which is a special case of a rhombus.)


How are parallelogram and a rhombus different?

All four sides of a rhombus are the same length. In a parallelogram there are two pairs of sides with equal lengths but one pair is different from the other pair.


Have four side soppostie sides are equal in length tow pair of parallel sides not have right angles?

A parallelogram.


What is a quadrilateral with four sides in which each pair of opposite sides are parallel and equal in length?

That quadrilateral is known as a 'parallelogram'.