Problem The two regular polygons ABCDEF and JKI have the same perimeter. What is the ratio of their areas? Solution Since you are comparing areas of polygons, the most efficient solution would be to dissect them into congruent shapes. That is, show that both polygons can be tessellated or tiled by the same shape. Of…

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Here are three important theorems about triangles: sum of angles of a triangle, the measure of the exterior angle, and the base angles of an isosceles triangle. Sample problems where these are applied are also provided. The problems involved the concept of ratio. Theorem: The Sum of the Angles of a Triangle The sum of…

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The probability of a spinner stopping at a certain area is the ratio of that area to the area of the entire region. Here is a question about comparing probabilities to test your understanding of this concept. Problem Four students are examining three spinners. They are discussing the probabilities of the spinners stopping at the…

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It is always assumed that a sample has all the characteristics of the population from which it is taken. For example, if it is given that the ratio of men to women in a population is 2:3 or 40% to 60%, the same will be true to the sample. Problem A survey has shown that…

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