Proof by contradiction. Practice
Answers are for parents and teachers.
1
Write the opposite of “only one line passes through two points” (not a proof, just the assumption).
At least two different lines pass through two points.
2
A 25° angle is laid on a ray in both half-planes. What is the total angle between the two outer sides?
50
3
A staircase has angle 55°. Why is it less comfortable?
55° is above the comfortable range 30°–45°; it is steep to climb.
4
Try to prove “two perpendiculars to a line do not intersect” by contradiction in your own words.
If they intersected, laying the right angles into the other half-plane gives a second common point; then two lines pass through two points, contradicting the axiom.
5
Find 3 examples of perpendicular lines around you (e.g. a notebook grid).
For example: notebook grid, window frame, door corner.