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# Can two identical trapezoids form a parallelogram?

## Can two identical trapezoids form a parallelogram?

You can put two identical trapezoids together to form a parallelogram with the same height as the trapezoid and a base length equal to the sum of the base lengths of the trapezoid. The area of the parallelogram is (b1 + b2)h, so the area of the trapezoid is one-half of this area.

## Can a parallelogram be divided?

The Diagonals Divide a Parallelogram Into Four Equal Areas Since those two triangles are congruent, their areas are equal. We also saw that the diagonals of the parallelogram bisect each other, and so create two additional pairs of congruent triangles.

Do all parallelograms have 2 equal sides?

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

### How do you divide a parallelogram into three equal parts?

If each of these two triangles is divided by a line parallel to that diagonal of the parallelogram such that one-third of the area is between the line and the diagonal, then the two lines constructed in this way will be the desired lines to divide the parallelogram into three equal areas.

### Is triangle a parallelogram?

A triangle is a parallelogram. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

What makes parallelogram a triangle?

A parallelogram can always be decomposed into two identical triangles by a segment that connects opposite vertices. To produce a parallelogram, we can join a triangle and its copy along any of the three sides, so the same pair of triangles can make different parallelograms.

#### Are all 4 sides of a parallelogram equal?

Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. Definition 3: A rhombus is a quadrilateral where all four sides have the same length.

#### Is every rectangle a special parallelogram?

A rectangle is a quadrilateral with four right angles. Therefore, every rectangle is a parallelogram . The diagonals of a rectangle are congruent and bisect each other. A rhombus is a quadrilateral with four congruent sides.

What is the difference between a trapezoid and a parallelogram?

As nouns the difference between parallelogram and trapezoid. is that parallelogram is (geometry) a convex quadrilateral in which each pair of opposite edges are parallel and of equal length while trapezoid is (geometry) a (convex) quadrilateral with two (non-adjacent) parallel sides.

## Is every trapezoid a rhombus?

Every rhombus is a parallelogram and a trapezoid. Appart from it you can say that: Parallelogram is trapezoid, but not every trapezoid is a parallelogram (for example a right trapezoid is not a parallelogram because it has only one pair of parallel sides) Rectangle is a parallelogram.

## What shapes are not a parallelogram?

If only one set of opposite sides are congruent, you do not have a parallelogram, you have a trapezoid. This means every parallelogram is: A plane figure (it has two dimensions) A closed shape (it has an interior and exterior) A quadrilateral (four-sided plane figure with straight sides)