Admin Table of Contents
- 1 Can a parallelogram be cut in half to form two triangles?
- 2 Can a parallelogram be divided?
- 3 Do opposite sides of a parallelogram have to be congruent?
- 4 In which parallelogram does the diagonal divide the parallelogram into two congruent right angles?
- 5 Are all parallelograms congruent?
- 6 Which two figures can always be described as quadrilaterals with all sides congruent?
Can a parallelogram be cut in half to form two triangles?
Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles.
Can a parallelogram be divided?
The Diagonals Divide a Parallelogram Into Four Equal Areas Each of the diagonals of a parallelogram divides it into two congruent triangles, as we saw when we proved properties like that the opposite sides are equal to each other or that the two pairs of opposite angles are congruent.
What of a parallelogram divides it into two congruent?
diagonal
So, all the corresponding sides and angles of one triangle are equal to that of the other. And AB = CD. Therefore, it is proved that the diagonal of a parallelogram divides it into two congruent triangles and also opposite sides of a parallelogram are equal.
Can 2 parallelograms be congruent?
Two parallelograms will be congruent only when all four corresponding sides are equal in length & one corresponding internal angle is equal.
Do opposite sides of a parallelogram have to be congruent?
If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.
In which parallelogram does the diagonal divide the parallelogram into two congruent right angles?
Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles. Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent….Theorems about Quadrilaterals.
| Statements | Reasons |
|---|---|
| @$\begin{align*}ABCD\end{align*}@$ is a parallelogram | Definition of a parallelogram |
What should be added to a parallelogram to make it into two congruent triangles?
Expert Answer:
- In BAC and DCA.
- 1 = 2.
- 3 = 4 [alternate pair]
- AC = AC (common)
- Therefore, diagonal of a parallelogram divides it into two congruent triangles.
Are parallelograms always congruent?
Parallelogram: A quadrilateral with two pairs of parallel lines. To start off with basic rules, opposite sides of a parallelogram are always equal length and parallel. Inside a parallelogram, opposite angles are always congruent.
Are all parallelograms congruent?
Opposite sides of parallelograms are congruent. Opposite angles of parallelograms are congruent. Adjacent angles of parallelograms are supplementary. One pair of opposite sides is both parallel and congruent.
Which two figures can always be described as quadrilaterals with all sides congruent?
All squares and rectangles have opposite sides that are congruent.