This is the marking copy and it carries every answer. Her sheet is the other file — same numbering, same margin codes, so you can mark straight down the page.
Which of the following figures has only ONE line of symmetry?
(1) a parallelogram (2) a regular pentagon (3) an isosceles trapezium (4) a rectangle
answer (3) — an isosceles trapezium
method Count the folds for each. A parallelogram has none — no fold makes its halves match. A regular pentagon has five. A rectangle has two, one across and one down. The isosceles trapezium has exactly one, straight down the middle.
watch Choosing the rectangle. It folds down the middle AND across the middle, so it has two, and the question asks for ONLY one.
Look at the figure below — shaded squares on a 6 × 6 grid, with a dashed diagonal line running from the bottom-left corner to the top-right. Which one of the options will form a symmetric figure with the above, about that dashed line?
the dashed line is the MIRROR. The option must hold the reflection of every shaded square across it — same distance from the line, other side.
(1) Option 1 (2) Option 2 (3) Option 3 (4) Option 4
answer (1) — Option 1
method The dashed diagonal is the mirror line. Take each shaded square above the line and count its steps to the line; its partner must be the same number of steps on the other side. Only option 1 places every partner correctly, including the half-shaded triangle, which must reflect into a triangle leaning the opposite way.
watch Checking only the big blocks and not the half-squares. The triangles are what separate option 1 from option 3 — they must flip, not just move.
A figure folded in half along the dotted line of symmetry is shown: below a horizontal dotted line sit two half-circles, each with one dot and a single stroke leaning to the right. Which of the following figures is the symmetric figure when opened up?
- - - - - - - - - - - - <- the fold line (horizontal) | ( . / ) ( . / ) | +------------------------------+ everything shown is the BOTTOM half; opening up mirrors it UPWARDS
(A) two faces, dots stacked, each with a stroke still leaning one way ( / ) (B) two faces, dots stacked, each with a curve bulging right ( ) ) (C) two faces, dots side by side, each with a smile underneath (D) two faces mirrored left-to-right — one ) and one (
answer (B) — two faces, dots stacked, each with a curve bulging right ( ) )
method The fold line is HORIZONTAL, so opening up reflects everything upwards. The single dot in each half-circle gains a partner directly above it, giving two dots stacked one over the other. The leaning stroke reflects too: a stroke leaning one way, joined to its mirror leaning the other way, makes a curve that bulges out to the right — a ) shape. Only B has both.
watch Picking D, which mirrors the two faces LEFT to RIGHT. The fold line drawn is horizontal, so the mirror is up-and-down, and both faces must end up identical to each other.
Four different shapes J, K, L and M are shown below. Which of the following figures are symmetrical?
/\ ______
/ \ / \
/ \ / \
/______\ /__________\
J K
________ ____
| | / /
| | / /
|________| /____/
L M
J isosceles triangle K isosceles trapezium
L square M slanted parallelogram(1) J and K only (2) J, K and L only (3) J, K and M only (4) J, K, L and M
answer (2) — J, K and L only
method Fold each shape and see whether the two halves land on each other. J (isosceles triangle) folds down the middle. K (isosceles trapezium) folds down the middle. L (square) folds four different ways. M is a slanted parallelogram — there is no fold that makes its halves match. So J, K and L only.
watch Thinking a parallelogram is symmetrical because it looks balanced. It has ROTATIONAL symmetry (turn it half-way round and it matches) but no LINE of symmetry — and this question asks about folding.