Which theorem can be used to prove that the quadrilateral is a parallelogram?
Table of Contents
- 1 Which theorem can be used to prove that the quadrilateral is a parallelogram?
- 2 Is it true that if two diagonals of a quadrilateral divide it into 4 triangles of equal area then the quadrilateral is a parallelogram?
- 3 Which statement proves that a quadrilateral is a rhombus?
- 4 When you divide a quadrilateral diagonal you will have?
Which theorem can be used to prove that the quadrilateral is a parallelogram?
Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent. 2. Now, let’s prove that if a quadrilateral has opposite sides congruent, then its diagonals divide the quadrilateral into congruent triangles….Theorems about Quadrilaterals.
| Statements | Reasons |
|---|---|
| Parallelogram \begin{align*}ABCD\end{align*} | Given |
Is it true that if two diagonals of a quadrilateral divide it into 4 triangles of equal area then the quadrilateral is a parallelogram?
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.
How do you write a proof of a parallelogram?
Well, we must show one of the six basic properties of parallelograms to be true!
- Both pairs of opposite sides are parallel.
- Both pairs of opposite sides are congruent.
- Both pairs of opposite angles are congruent.
- Diagonals bisect each other.
- One angle is supplementary to both consecutive angles (same-side interior)
How do you prove a quadrilateral?
Here are the six ways to prove a quadrilateral is a parallelogram:
- Prove that opposite sides are congruent.
- Prove that opposite angles are congruent.
- Prove that opposite sides are parallel.
- Prove that consecutive angles are supplementary (adding to 180°)
- Prove that an angle is supplementary to both its consecutive angles.
Which statement proves that a quadrilateral is a rhombus?
If all sides of a quadrilateral are congruent, then it’s a rhombus (reverse of the definition). If the diagonals of a quadrilateral bisect all the angles, then it’s a rhombus (converse of a property).
When you divide a quadrilateral diagonal you will have?
If Each Diagonal of a Quadrilateral Divides it in Two Triangles of Equal Area then Prove that the Quadrilateral is a Parallelogram.
When you divide a quadrilateral diagonal How many triangles?
two
Parallelogram Theorem #1 Converse: If each of the diagonals of a quadrilateral divide the quadrilateral into two congruent triangles, then the quadrilateral is a parallelogram.