Caffeine is the active ingredient in coffee and many energy drinks. once caffeine is consumed it
has a half-life in the body of approximately 4 hours. an average cup of coffee contains 100mg of
caffeine. suppose you drink a cup of coffee at 8am, followed by another cup at 10am and an
afternoon cup of coffee at 3pm. how much caffeine is left in your body when you go to sleep at
11pm?

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.