Given ABCD is a parallelagram diagonals AC and BD intersect at E Prove AE is congruent to CE and BE is congruent to DE
2 answers:
In the parallelogram ABCD, diagonals AC and BD intersect at point E.
According to the definition of parallelogram, opposite sides are equal and parallel to each other. That means, AB = DC
Now as AB and DC are parallel, so according to the property of Alternate Interior Angles, we will get:
∠EAB = ∠ECD and ∠EBA = ∠EDC
Thus , in two triangles ΔABE and ΔDCE, two angles and one side are equal. So, ΔABE and ΔDCE are congruent to each other.
That means, AE = CE and BE = DE
So, AE is congruent to CE and BE is congruent to DE
You might be interested in
The answer could be 3/2 or 1/4 and I don’t know if this is right
As we can see in the given figure, Angles A and B are equal. therefore their opposite sides will be equal to one another, that is ~
- AB = BC
now, let's plug the values of AB and BC in terms of x and equate them to find the value of x ~
now , let's find the measure of side AC ~
- AC = 6x + 7
that is ~
We start with the parent function
The first child function would be
We have multiplied the input of the function by a constant: we have
This kind of transformation result in a horizontal stretch/compression. If the multiplier is greater than 1, we have a compression. So, this first child causes a horizontal compression with compression rate 2.
The second child function would be
We added 6 to the input of the function: we have
This kind of transformation result in a horizontal translation. If the constant added is positive, we translate to the left. So, this second child causes a translation 6 units to the left.
The third child function would be
We changed the sign of the previous function (i.e. we multiplied it by -1): we have
This kind of transformation result in a vertical stretch/compression. If the multiplier is greater than 1 we have a stretch, if it's between 0 and 1 we have compression. If it's negative, we reflect across the x axis, and then apply the stretch/compression. In this case, the multiplier is -1, so we only reflect across the x axis.
The fourth child function would be
We added 3 to previous function: we have
This kind of transformation result in a vertical translation. If the constant added is positive, we translate upwards. So, this last child causes a translation 3 units up.
Recap
Starting from the parent function , we have to:
- Compress the graph horizontall, with scale factor 2;
- Translate the graph 6 units to the left;
- Reflect the graph across the x axis;
- Translate the graph 3 units up
Note that the order is important!