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Is a quadrilateral a parallelogram if both pairs of opposite sides are equal?
Wiki User
∙ 14y ago
Yes.
Although the definition of a parallelogram is "a quadrilateral with both pairs of opposite sides parallel", the only way for a quadrilateral to include opposite sides of equal length is if the included angles are the same, and hence the sides are parallel.
(Hint : draw a diagonal to a parallelogram. You can show that one of the two triangles formed is the mirror image of the other, which immmediately proves that each pair of opposite sides is equal.)
Wiki User
∙ 14y ago
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Do a parallelograms diagonals bisect each other?
I can't offer a full proof, but I can suggest some possibilities that will lead you to your proof. In a parallelogram, you can easily demonstrate that the angles formed by a cord extending between parallel lines and the parallel lines themselves, and that are formed on opposite sides of the cord, are equal. This will work for both pairs of triangles in the parallelogram, and can be applied to all of the angles at the corners of the parallelogram. This will lead you to demonstrating that the pairs of triangles "pointing" to each other (not adjacent pairs) are similar, and in fact congruent. From there it is not difficult to establish that the connected sections of the two interior cords are equal.
What are the similarities between a parallelogram and a rectangle?
A rectangle is a parallelogram. However, parallelograms only need two sets of parallel lines, not necessarily with all right angles as in the rectangle : they can also be rhomboids and rhombi. The shared features are - parallel opposite sides - equal opposite angles - supplementary adjacent angles
How does a trapezoid differ from a parallelogram?
A trapezoid has one pair of parallel sides. A parallelogram has two pairs of parallel sides.
Are the words little and large opposites?
Yes, those words are antonyms. However, the antonym pairs are usually - little, opposite of big - small, opposite of large
What times what equal 44?
The numbers below are the factor pairs of 44. Multiplied together they equal 44: (1, 44) (2, 22) (4, 11)
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.
A quadrilateral is a parallelogram only if both pairs of opposite sides are equal?
true
What is a quadrilateral with 2 pairs of opposite equal sides and no lines of symmetry?
A parallelogram.
Is A quadrilateral is a parallelogram only if both pairs of opposite sides are equal?
true
Can a quadrilateral be a parallelogram?
Yes, because a square is a parallelogram
What ia a parallelogram?
A parallelogram is a geometric quadrilateral with two pairs of parallel sides. The opposite sides and opposite angles are equal in length.
If a quadrilateral is a parallelogram will it always have equal angles?
Diagonally opposite pairs of angles will always be equal, but the only time all angles in a quadrilateral parallelogram are equal is when that shape is a rectangle.
A parallelogram is a quadrilateral in which both pairs of opposite sides are paraellel?
Yes. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.
What is the Parallelogram Opposite Sides Converse?
If a quadrilateral has two pairs of opposite congruent sides, then the quadrilateral is a parallelogram.
What quadrilateral has 2 pairs of sides with equal length and 2 pairs of opposite parallel sides?
A parallelogram is such a shape.
What makes a quadrilateral a parallelogram?
A quadrilateral is a parallelogram if it has two pairs of (opposite) sides that are parallel.
A quadrilateral with both pairs of opposite sides congruent?
A quadrilateral with both pairs of opposite sides congruent is a parallelogram.
