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draw a diagonal through opposite corners of the quadrilateral. This makes two triangles. Prove the triangles are congruent using SSA (side side angle) congruence. Then show that the other two sides of the quadrilater must be congruent to each other, so it is a parallelogram.

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โˆ™ 2010-01-25 22:26:54
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Q: If one pair of opposite angles and one pair of opposite sites of a quadrilateral is congruent then the quadrilateral is a parallelogram. How can it be proven?
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Related questions

If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is not a parallelogram?

False. If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram.


If one pair of opposite angles of a quadrilateral are congruent and one pair of opposite angles are congruent then is the quadrilateral a parallelogram?

For the quadrilateral to be a parallelogram, both pairs of opposite angles must be congruent.


Can congruent angles determine if there is a parallelogram?

If both pairs of opposite angles of a quadrilateral are congruent, then it is a parallelogram.


What is a quadrilateral that has opposite angles congruent?

Every parallelogram is.


What is a quadrilateral with 2 pairs of opposite congruent angles?

a parallelogram


If both pairs of opposite angles of a quadrilateral are congruent is the quadrilateral a parallelogram?

Yes


If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram?

True


Conditions which guarantee that a quadrilateral is a parallelogram?

Theorem A: A quadrilateral is a parallelogram if its opposite sides are congruent. Theorem B: A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent. Theorem C: A quadrilateral is a parallelogram if its diagonals bisect each other. Theorem D: A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.


What is a quadrilateral with two pair of opposite angles congruent called?

parallelogram


If one pair of opposite angles of a quadrilateral is congruent then the quadrilateral is a parallelogram?

false; if both pairs


What quadrilateral has two pairs of opposite congruent sides and four congruent angles?

A parallelogram has the 2 pair of opposite congruent sides, but a rectangle (special case of parallelogram) also has the four congruent angles.


What is the ways to prove that a quadrilateral is a parallelogram?

If it is a parallelogram, then it has two sets of parallelogram sides. Parallelograms' opposite angles are congruent A parallelogram's bisectors are congruent. * * * * * A parallelogram's bisectors are NOT congruent.

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