There are five ways to prove that a quadrilateral is a parallelogram:
- Prove that both pairs of opposite sides are congruent.
- Prove that both pairs of opposite sides are parallel.
- Prove that one pair of opposite sides is both congruent and parallel.
- Prove that the diagonals of the quadrilateral bisect each other.
How do you prove that a rectangle is a parallelogram?
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. Its diagonals bisect each other.
How to prove that a parallelogram is 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) 6 One pair of opposite sides are congruent AND parallel
How are two parallel angles supplementary in a parallelogram?
In a parallelogram, any two consecutive angles are supplementary, no matter which pair you pick. Parallelograms are special types of quadrilaterals with opposite sides parallel. Parallelograms have these identifying properties: Parallelograms get their names from having two pairs of parallel opposite sides.
Can a quadrilateral really be a parallelogram?
Sometimes in geometry, something you think you know, like a parallelogram, may really be something else, like only a quadrilateral. Here are six ways to mathematically prove a given quadrilateral is a parallelogram. Quadrilaterals are four-sided, closed polygons. Their sides can be of any length, their angles either congruent or not.
How to prove that both pairs of opposite sides are parallel?
Prove that both pairs of opposite sides are parallel. Prove that both pairs of opposite sides are congruent. Prove that one pair of opposite sides is both congruent and parallel. Prove that the diagonals bisect each other.
