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Use Inductive Reasoning To Identify Patterns And Make Predictions

True or False: After examining the first few terms of a sequence (3, 9, 27, 81, ...), you conjecture that the nth term is obtained by multiplying each previous term by 3.

True or False: After measuring the angles in several right-angled triangles, you find that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, you conjecture that the Pythagorean Theorem holds for all right-angled triangles.

True or False: After examining the side lengths of several rectangles, you find that opposite sides are always equal. Therefore, you conjecture that all rectangles have opposite sides of equal length.

True or False: After examining the first few terms of a sequence (1, 4, 9, 16, ...), you conjecture that the nth term is obtained by squaring consecutive natural numbers.

True or False: After analyzing the side lengths of several triangles, you notice that the sum of the lengths of any two sides is always greater than the length of the third side. Therefore, you conjecture that the Triangle Inequality Theorem holds for all triangles.

True or False: After measuring the angles formed by intersecting lines, you observe that vertical angles are always congruent. Therefore, you conjecture that all vertical angles are congruent.

True or False: After studying the first several terms in a sequence (2, 4, 8, 16, ...), you conjecture that the nth term is obtained by multiplying each previous term by 2.

True or False: After measuring the angles in several regular polygons, you find that the sum of interior angles can be calculated using the formula (n - 2) * 180, where n is the number of sides. Therefore, you conjecture that this formula holds for all regular polygons.

True or False: After examining the first few terms of a sequence (1, 3, 7, 15, ...), you conjecture that the nth term is obtained by doubling the previous term and adding 1.

True or False: After measuring the interior angles of several quadrilaterals, you find that their sum is always 360 degrees. Therefore, you conjecture that the sum of interior angles in any quadrilateral is 360 degrees.