Table of Contents

- 1 Does a diagonal of a parallelogram forms two congruent triangles?
- 2 When you draw a diagonal of any parallelogram what type of triangles do you get?
- 3 Do 2 isosceles triangles make a parallelogram?
- 4 Which parallelogram does the diagonal divide the parallelogram?
- 5 Why are the diagonals of a parallelogram not congruent?
- 6 When a diagonal bisects a parallelogram does it produce two?

## Does a diagonal of a parallelogram forms two congruent triangles?

Diagonal AC divides the parallelogram into two triangles △ABC and △ADC. 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.

## When you draw a diagonal of any parallelogram what type of triangles do you get?

two congruent triangles

Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles.

**What is formed if a diagonal is drawn in a parallelogram?**

The diagonals in a parallelogram bisect each other. When one diagonal is drawn in a parallelogram, two congruent triangles are formed. When two diagonals are drawn in a parallelogram, two pairs of congruent triangles are formed.

**What is show that each diagonal divides the parallelogram into two congruent?**

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 |
---|---|

Parallelogram @$\begin{align*}ABCD\end{align*}@$ | Given |

### Do 2 isosceles triangles make a parallelogram?

A pair of isosceles triangles forms two different parallelograms because its two equal sides form the same parallelogram and its third side forms a different parallelogram. A pair of scalene triangles forms three different parallelograms because its sides all have different lengths. 3.

### Which parallelogram does the diagonal divide the parallelogram?

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 |

**Is diagonal of parallelogram bisect each other?**

Theorem: The diagonals of a parallelogram bisect each other.

**Are the diagonals of a parallelogram always congruent?**

They will see that the diagonals are always congruent, but not always perpendicular. A rhombus is shown on page 1.6. Remind students that a rhombus is a parallelogram with four congruent sides. Like a rectangle, it holds all of the characteristics of a parallelogram, but may have more.

## Why are the diagonals of a parallelogram not congruent?

Diagonals in Parallelograms Parallelogram diagonals are drawn from one opposite side of the parallelogram to the other. This occurs because the opposite angles of a parallelogram are congruent. The diagonals themselves will not be congruent to each other unless the parallelogram is also a square or a rhombus.

## When a diagonal bisects a parallelogram does it produce two?

The diagonals of a parallelogram bisect each other. The diagonals of a rhombus intersect at right angles. A diagonal of a rectangle divides it into two congruent right triangles.

**In which parallelogram does the diagonal divide the parallelogram into two congruent right angles?**