L3 · Lines and angles clinic
“I can move fluently between the two halves of this unit: given one angle where a transversal cuts parallel lines I can produce any other angle and justify it, and given any angle - including reflex angles - I can classify it, estimate it, measure it, copy it and bisect it. I can also check a real corner for square (perpendicular) using a 3-4-5 triangle.”
Lines m and n are parallel, angle 1 = 55°. Produce angles 7, 8 and 3, each with its justification. Angle 7: alternate exterior to angle 1, so 55°. Angle 8: linear pair with angle 7, so 180 - 55 = 125°. (Also co-exterior with angle 1: 55 + 125 = 180 - two routes, one answer.) Angle 3: vertically opposite angle 1, so 55°. (Also corresponding to angle 7.) Say it plainly: start from the given angle, name each relationship BEFORE you compute, and cross-check with a second route whenever one exists.
Angle 8 was found by two different routes that must agree because...
With angle 1 = 55°, find angle 5 and justify two ways. -> 55° - corresponding to angle 1 (same corner, upper-left), and vertically opposite angle 7 (55°)
"Angle 6 is co-interior with angle 3 (55°), so angle 6 = 180° - ___ = ___." -> 55°; 125°
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.