Why are the opposite sides of a parallelogram equal?

Why are the opposite sides of a parallelogram equal?

Each pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram, so: Its opposite sides are equal and parallel.

Why opposite sides are congruent?

Opposite Sides Are Congruent If you were to superimpose the shapes on top of each other they would match up exactly. This is true for a parallelogram’s sides. Each of the opposite sides are the same in length.

Is it true that the opposite sides of a parallelogram are congruent?

1. Opposite Sides Theorem Converse: If both pairs of opposite sides of a quadrilateral are congruent, then the figure is a parallelogram.

How do you prove that the opposite sides of a parallelogram is equal?

TrueTrue – The diagonals of a rectangle are always equal and perpendicular. FalseFalse – The diagonals of a rectangle are always equal and perpendicular. A diagonal of a parallelogram divides it into two congruent triangles. TrueTrue – A diagonal of a parallelogram divides it into two congruent triangles.

Are the opposite sides of a parallelogram parallel?

Definition 1: A parallelogram is a four sided figure where the opposite sides are parallel. Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other. Theorem 4: If one pair of opposite sides in a four sided figure are both opposite and parallel, then the figure is a parallelogram.

Why are opposite angles congruent?

Opposite angles are also congruent angles, meaning they are equal or have the same measurement. Two crossing lines actually create two sets of opposite angles that, when the measures of their angles are added all together, will equal 360 degrees and make a circle.

Are opposite sides of parallelogram parallel?

Opposite sides of a parallelogram are parallel (by definition) and so will never intersect. The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

How do you prove a parallelogram is congruent?

Well, we must show one of the six basic properties of parallelograms to be true!

1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. Both pairs of opposite angles are congruent.
4. Diagonals bisect each other.
5. One angle is supplementary to both consecutive angles (same-side interior)

What are adjacent angles in a parallelogram?

Adjacent angles in a parallelogram are always supplementary. Supplementary means the angles have a sum of 180 degrees. So if your first angle is 40 degrees the next angle would be 140 degrees. Rectangles are a subset of parallelograms.

How many sides on a parallelogram?

A parallelogram is a two-dimensional rhomboid or quadrilateral with four sides. The four sides, or edges, consist of two pairs, each with the opposite side parallel and congruent. The two pairs of consecutive angles, or vertices, in a parallelogram are supplementary, which means that the sum of the angles in each consecutive pair is 180 degrees.

What shapes are parallelograms?

Parallelograms are shapes that have four sides with two pairs of sides that are parallel. The four shapes that meet the requirements of a parallelogram are square, rectangle, rhombus, and rhomboid.

Is a quadrilateral always a parallelogram?

A parallelogram is a polygon with 2 pairs of opposite parallel sides. A quadrilateral can be a parallelogram but not always. For example – rectangles, squares, and rhombi all have 4 sides and 2 pair of parallel sides so they are both parallelograms and quadrilaterals.