The diagram shows ABCD, where a ≠ b, a ≠ 0 and b ≠ 0.
2 answers:
C. ABCD is a trapezoid, but it is not an isosceles trapezoid.
Step-by-step explanation:
ABCD is a trapezoid not an isosceles trapezoid. Because opposite sides of isosceles trapezoid are parallel.
The characteristics of trapezoid are legs, lower base angles, upper base angles diagonals are congruent.
The characteristics of isosceles trapezoid are bases are parallel, opposite sides are same length.
From the above mentioned characteristics of an Trapezoid and Isosceles trapezoid the given is trapezoid.
Given data clearly mentioned in diagram ABCD, where a≠b, a≠0 and b≠0 So, it is trapezoid.
Result:
So, the given is Trapezoid not an isosceles trapezoid . Because ABCD, where a≠b, a≠0 and b≠0.
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<h2>Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:
where n is a positive integer.
- Let us take n=1
then we have:
Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.
- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u>
Let us take n=k+1
Hence, we have:
( Since, the result was true for n=k )
Hence, we have:
Also, we know that:
(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,
Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.