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If the ratio of one side and one leg of the left-hand triangle is the same ratio as the corresponding side and leg of the right-hand triangle, they are proportional to each other, so they are similar. The right triangle has 30 cm legs and a 20 cm third side. Notice the left triangle has two legs 15 cm long and a third side, 10 cm long. Recall that the equal sides of an isosceles triangle are called legs. Next, you have to compare corresponding sides to see if they maintain the same ratio. You check and the corresponding angles between legs and third sides are congruent, at 71°. Are they similar? You have to check their interior angles to see if they are the same in both isosceles triangles. Are they similar?īelow are two isosceles triangles, one with sides twice as long as the other. Or like your dog Bailey and the neighborhood dog Buddy.Ĭongruent objects are also similar, but similar objects are not congruent. A shoe box for a size 4 child's shoe may be similar to, but smaller than, a shoe box for a man's size 14 shoe. Two geometric shapes are similar if they have the same shape but are different in size. Our example may sound a bit silly, but in geometry we use transformations all the time to bring two objects near each other, turn them to face the same way, and, if necessary, flip them to see if they are similar. You would have to wake Bailey up and get the two dogs facing the same direction, so you could compare snouts, and ears, and tails. (15 points)Ī) The sequence is monotonic and bounded.You could bring Bailey and Buddy together. Use the graph of the function f of x equals x plus 1 over x to determine which of the following statements is true for the sequence a sub n equals the sequence n plus 1 over n. If a geometric sequence is identified, state If an arithmetic sequence is identified, state its common difference. Investigate whether A + B andĪ x B are arithmetic or geometric sequences. Which term if the geometric sequence 18,54,162,486. Please give the answers and solutions for each.ġ.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term.Use the graph of the function f of x equals 2 plus 1 over x to determine which of the following statements is false for the sequence a sub n equals the sequence 2 plus 1 over n.What would be the price of a sweater after 8 discounts? Is this an arithmetic or geometric sequence? 0625 form a series of 5 consecutive terms in a geometric sequence? Select all that applyĪ store manager plans to offer discounts on some sweater acording to this sequence: $48, $36, $27, $20.255. Which of the following three numbers, inserted between 16 and.geometric, 1, 1/3, 1/9 What are the first four terms of an arithmetic sequence if the common Find the common ratio of the geometric sequences.ġ. The first, third and ninth terms of an arithmetic sequence form the terms of a geometric sequence.Is this series convergent or divergent? If it is convergent, what value of x yields an infinite sum of 1085/13? Ī different geometric sequence has r = -6/7 and the first term is denoted x. Eric thinks of 2 sequences.One is geometric and the other arithmetic.Both sequences start with the number 3.The common ratio of the geometric sequence is the same as the common difference of the arithmetic sequence.If the 6-th term of the geometric.
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