Mathematics, 07.10.2020 07:01 oneicyahdaley10

In the pattern shown, each small triangle is an equilateral triangle with an area of 1 square unit. a. Explain how you know that any triangle made out of equilateral triangles is equilateral. To form a triangle, each side will be made out of number of sides of the original equilateral triangle. Also, the angles of any triangle formed will be congruent. By the , if a triangle is equiangular, then it is . Question 2 b. Find the areas of the first four triangles in the pattern. Area of Triangle 1: units2 Area of Triangle 2: units2 Area of Triangle 3: units2 Area of Triangle 4: units2 Question 3 Describe the pattern of the areas. Predict the area of the seventh triangle in the pattern. Explain your reasoning. Let An represent the area of the nth triangle. Then by inductive reasoning, the pattern of the areas is An= square units. So, the area of the seventh triangle is A7= square units.

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In the pattern shown, each small triangle is an equilateral triangle with an area of 1 square unit....

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