Grade 10 — Mathematics 10-3 › T3U08 Lines & Angles

Grade 10 › T3U08 Lines & Angles › L1
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-G5

L1 · Parallel, perpendicular and transversal lines: angle pairs

Learning goal

“I can name every pair of angles formed when a transversal cuts two lines, and - when the lines are parallel - I can find any angle from one given angle using corresponding, vertically opposite, alternate and same-side relationships. I can also explain why those shortcuts fail when the lines are not parallel.”

Transversal — a line that crosses two or more other lines, like a diagonal brace crossing two rails.
Corresponding angles — angles in the same corner position at each crossing (angle 2 and angle 6 are both upper-right). Equal when the lines are parallel.
Alternate interior angles — angles between the two lines, on opposite sides of the transversal (angles 4 and 6; angles 3 and 5). Equal when the lines are parallel.
Vertically opposite angles — the angles directly across from each other at one crossing (angles 2 and 4). Always equal, parallel or not.
Worked example

Lines m and n are parallel, cut by transversal t. Angle 2 measures 115°. Find angles 6, 5 and 4. Angle 6 is in the same corner (upper-right) at the lower crossing: a corresponding angle. Parallel lines make corresponding angles equal, so angle 6 = 115°. Angle 5 sits beside angle 6 on the straight lower line: a linear pair, so the two sum to 180°. Angle 5 = 180° - 115° = 65°. Angle 4 is directly across the upper crossing from angle 2: vertically opposite angles, always equal. Angle 4 = 115°. Say it plainly: on parallel lines, every angle is either equal to the given angle or supplementary to it (180° minus it). There are only two sizes at the crossings.

Check yourself — explain it

Angle 5 came out supplementary to angle 2 even though they are at different crossings because...

Paired problem — example still visible

With angle 2 = 115°, find angle 3 and say which relationship you used. -> 65° - angle 3 is a linear pair with angle 2 at the same crossing (or vertically opposite angle 1)

Faded completion — last step is yours

"Angle 7 equals angle 3 because they are ___ angles, so angle 7 = ___." -> Corresponding; 65°

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