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
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After 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
<h3>What is an exponential function?</h3>It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent.
where a is a constant and a>1
We have:
A philanthropist pledges to donate 10% of a fund each year.
We can find the amount left after 7 years as follows:
A = 450000(1 - 0.1)⁷
10% of a fund each year.
Rate r = 10% = 0.1
A = 450000(0.9)⁷
A = $2152336.05
Thus, after 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
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