Prove that the diagonals of a rectangle bisect each other. the midpoint of is _____
1 answer:
In this attached picture, we can prove that triangles AOB and COD are congruent. ∠CDO and ∠ABO are equal because they are alternate angles. Similarly, ∠OAB and ∠OCD are equal because they are alternate angles, as well. We have a rectangle and in the rectangle, opposite sides are equal; AB = CD. Then, because of Angle-SIde-Angle principle, we can say that triangles AOB and COD are equal. If triangles are congruent, then OD = OB and OC = AO. Applying congruency to the triangles ACD and BCD, we can see that these triangles are also congruent. It means that the diagonals are equal. Since, OD = OB and OC = AO, it proves that the point O simultaneously is the midpoint and intersection point for the diagonals.
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Answer 1:
It is given that the positive 2 digit number is 'x' with tens digit 't' and units digit 'u'.
So the two digit number x is expressed as,
The two digit number 'y' is obtained by reversing the digits of x.
So,
Now, the value of x-y is expressed as:
So, is equivalent to (x-y).
Answer 2:
It is given that the sum of infinite geometric series with first term 'a' and common ratio r<1 =
Since, the sum of the given infinite geometric series = 200
Therefore,
Since, r=0.15 (given)
a=170
The nth term of geometric series is given by .
So, second term of the series = = ar
Second term =
= 25.5
So, the second term of the geometric series is 25.5
Step-by-step explanation: