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frosja888 [35]
2 years ago
11

Determine which postulate can be used to prove that the triangles are congruent. If it

Mathematics
1 answer:
Misha Larkins [42]2 years ago
6 0

Answer:

not possible

Step-by-step explanation:

You are told that one side of each triangle is congruent, and we know that vertical angles are congruent, therefore you have SA. SA does not determine similarity, so it is not possible with the amount of information given.

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Determine formula of the nth term 2, 6, 12 20 30,42​
nalin [4]

Check the forward differences of the sequence.

If \{a_n\} = \{2,6,12,20,30,42,\ldots\}, then let \{b_n\} be the sequence of first-order differences of \{a_n\}. That is, for n ≥ 1,

b_n = a_{n+1} - a_n

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b_{n+1} = b_n + 2

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and so on down to

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We solve for a_n in the same way.

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a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))

a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))

and so on down to

a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2

\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}

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