The idea in brief. FOLDING MAKES EQUAL ANGLES. The folded image of an angle is the same size as the angle it came from, so a deduction may cross the crease, and when it does, it is written as a line with its reason, exactly like every other property in this chapter. The crease is a line of symmetry (MOE P4 3.2), the folded vertex takes a prime, and `∠D′AE = ∠DAE` is the one line in the whole chapter that steps from one side of a fold to the other. In the lesson. A fold is a change of place, not a change of size.
Lesson video, with the working
Angles in a folded figure
2 min 34 s
The film teaches 1 question. The question shows first; its working is written as the film explains it.
Question 1 of 8 · Basic · free to tryABCD is a rectangular piece of paper. Corner D is folded along the crease…ABCD is a rectangular piece of…
ABCD is a rectangular piece of paper. Corner D is folded along the crease AE, where E is on DC, so that D lands at D' on the paper. Angle D'AE = 24°. Find angle AED.
∠AED = 180° − 90° − 24° = 66° (angle sum of triangle ADE)
Answer: 66°
Question 8 of 8 · Challenge · free to tryABCD is a rectangular piece of paper. Corner D is folded along the crease…ABCD is a rectangular piece of…
ABCD is a rectangular piece of paper. Corner D is folded along the crease AE, where E is on DC, so that D lands at D' on the paper. Angle D'AE = 24°. Find angle D'EC.
∠AED = 180° − 90° − 24° = 66° (angle sum of triangle ADE)
∠D'EC = 180° − 66° − 66° = 48° (angles on a straight line DEC)
Answer: 48°
For parents
How do you solve folded paper angle questions in P6?
Folding questions apply the Primary 6 outcome on unknown angles in composite figures to paper that has been folded.
What your child learns here
Folding questions apply the Primary 6 outcome on unknown angles in composite figures to paper that has been folded. The crease works like a mirror line, so the folded angle and the original angle are always equal.
Know that a fold changes where an angle is, not how big it is, so the original and folded angles are equal.
Read the prime mark: D′, said 'D prime', is where corner D lands after the fold.
Use the fold's two equal angles together with angles on a straight line, a right-angled corner or a triangle's angle sum.
Keep track of which angle the question names, since a fold creates several angles that look alike.
Does the answer make sense?
A fold moves an angle but never changes its size, so the angle and its folded copy on either side of the crease must carry the same number. Any triangle the crease makes with the paper's edges still has angles totalling 180°, which gives your child a second test of the found angle.
How to practise these questions
Basic questions train the key fact that a fold makes two equal angles, then finish with a straight line or a triangle. Intermediate questions add folds in rectangles, strips and parallelograms where the equal angles must be combined with parallel edges. In the Challenge questions the equal-angle fact is used twice, or the answer comes after working back through a right angle. If a folded angle has your child puzzled, read the written step-by-step solution.
Questions parents ask
Why are the folded angles equal? Folding moves the paper without stretching it, so every angle keeps its size. The crease acts as a line of symmetry between the original part and the folded part.
What does D′ mean on a folded figure? D′ is read 'D prime'. It marks where corner D lands after the fold, so the angle at D′ matches the angle that was at D.
Is folding in the P6 syllabus? Folding is not named as a separate outcome. These questions apply the Primary 6 outcome on finding unknown angles in composite figures to paper that has been folded.
