In algebra, we learn about functions of various types. these functions are often seen in a progression from least complicated (linear) to most complicated (piecewise with nonlinear parts). and then there are other types of functions in-between: exponential, quadratic, polynomial, radical, and logarithmic. but with all their differences and unique properties, these share a common trait of being functions that we can graph in a coordinate plane. what are some other things you can observe to have that same quality of functions: unique, but sharing a common trait or purpose?

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.