g10-14-05 · Additional mathematics
Perpendicular planes do not make every line normal
If two planes are perpendicular, is every line of one perpendicular to the other?
1 MIN · PREDICT ON PAPER
Fold a page to90°. Compare the crease direction with a line across the upright page.
Discuss or write first. No typed answer is required to continue.
A plane relation does not replace checking the selected line.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
Perpendicular planes contain some lines normal to the other plane, but the common hinge line lies in both planes. Other directions can be oblique.
Conditions: Use the angle between the planes; at fold0° or180° the planes coincide. A candidate line must be tested separately.
Mathematical justification: Let the hinge be x and the folded direction v=(0,cosα,sinα). The planes are perpendicular at α=90°, but the hinge x remains horizontal; only suitable transverse lines are vertical.
1 MIN · EXIT CHECK
In two perpendicular planes, is their intersection line perpendicular to either plane?
Check after answering
No; it lies in both planes.
Teacher guidance and extension
Before: Points, lines, planes and vector directions.
Ask: What does the common intersection line immediately disprove?
Watch for: Changing a statement about planes into a statement about every line in a plane.
Challenge: Find a line in the upright plane that makes45° with the floor.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
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