How do you prove that the diagonal of a parallelogram divides it into two congruent triangles?
How do you prove that the diagonal of a parallelogram divides it into two congruent triangles?
Answer
- Given: Parallelogram = ABCD. Diagonal = AC.
- To Prove: Diagonal of a parallelogram divides it into two congruent triangles.
- Solution: In ΔABC and ΔACD. AB || CD and AC is a transversal. Thus, ∠ ACB = ∠ CAD. AC = AC (common side) ∠CAB = ∠ ACD. Thus, by ASA congruency ΔABC ≅ ΔACD.
Does a diagonal of a parallelogram forms two congruent triangles?
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. You can show that alternate interior angles are congruent and hence lines are parallel for this part of the proof.
Is diagonal of parallelogram are equal?
The diagonals of a parallelogram are not of equal length. They bisect with each other at the point of intersection with equal sides across the point of intersection.
What is a diagonal of a parallelogram?
The diagonals of a parallelogram are the connecting line segments between opposite vertices of the parallelogram. Using this formula we can find out the lengths of the diagonals only using the length of the sides and any of the known angles.
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 |
How do I find the diagonal of a parallelogram?
Explanation: In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for . \displaystyle 20 – 3x = 2x – 4 \rightarrow 24 = 5x \rightarrow 4.8 = x. Then, substitute 4.8 for in each labeled segment to get a total of 11.2 for the diagonal length.