RAS question
A rectangular paper is folded once along its length. A right-angled triangle is cut from one corner of the folded edge. When unfolded, the cut-out shape will be:
Correct answer: (B) An isosceles triangle.
When the folded rectangular paper is opened, the cut-out is an isosceles triangle because the fold reflects the right-angled triangular cut onto the other half.
Explanation
The paper has been folded once along its length, so the folded edge acts as a line of reflection. NCERT's toy-based pedagogy material explicitly treats paper folding and cutting as a way to show symmetry by reflection. Here, the visible cut is a right-angled triangle made at one corner of the folded edge. When the paper is opened, the same cut appears on the other side as its mirror image. The two reflected halves share the fold line, so the combined opening is not just the original right-angled triangle; it becomes a symmetric triangle with two equal sides, which is an isosceles triangle.
Why the other options are wrong
- (A) A single right-angled triangle would be left only if there were no folded layer creating a reflected matching half.
- (C) A kite shape would need two pairs of adjacent equal sides, whereas this cut produces two mirror halves forming one isosceles triangle.
- (D) A parallelogram requires opposite sides to be parallel, but the mirrored triangular cut around the fold forms a triangle, not a four-sided figure.
Concept
This tests mental folding, cutting and mirror symmetry, a recurring reasoning area because RAS papers often ask candidates to visualise the final shape without drawing every step.