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Use Inductive Reasoning To Support Conjectures

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 doubling each previous term.

True or False: After measuring the angles in several polygons, you find that the sum of exterior angles is always 360 degrees. Therefore, you conjecture that the sum of exterior angles in any polygon is 360 degrees.

True or False: After examining the first few terms of a sequence (1, 3, 6, 10, ...), you conjecture that the nth term is obtained by adding consecutive natural numbers.

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


True or False: After measuring the interior angles of several triangles, you observe that their sum is always 180 degrees. Therefore, you conjecture that the sum of interior angles in any triangle is 180 degrees.

True or False: After measuring the angles in several rectangles, you find that opposite angles are always congruent. Therefore, you conjecture that all rectangles have congruent opposite angles.

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 measuring the angles in several isosceles triangles, you find that the base angles are always congruent. Therefore, you conjecture that all isosceles triangles have congruent base angles.

True or False: After analyzing the first ten terms in a number pattern (3, 6, 12, 24, ...), you conjecture that the nth term is obtained by multiplying each previous term by 2.

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.