The required relation between the angles m∠1 + m∠4 = 180°
Given that,
AB || DC and m∠2 ≅ m∠4
Prove: AD || BC
We have to determine,
The relation between the angles.
According to the question,
The opposite sides are parallel and congruent. The opposite angles are congruent. The consecutive angles are supplementary.
Each diagonal bisects the parallelogram into two congruent triangles.
Therefore, AD || BC
The two angles of a linear pair , like ∠1 and ∠3 in the figure , are always supplementary. But, two angles need not be adjacent to be supplementary.
In the next figure, ∠1 and ∠4 are supplementary, because their measures add to 180° .
Therefore,
Supplementary angles are those angles that sum up to 180 degrees.
∠1 and ∠4 are supplementary, because their measures add to 180° .
m∠1 + m∠4 = 180°
hence, The required relation between the angles m∠1 + m∠4 = 180°
For more information about Parallelogram click the link given below.
https://brainly.com/question/17150120
