Choose five terms, some from geometry and some from other areas of mathematics, and give a precise definition of each. Then change each of those definitions so that it still describes the term but not precisely enough to avoid ambiguity. Formulate counterexamples, with sketches when feasible, that show how things could satisfy the less precise definitions but not match the intended terms.

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.