2D Shapes: Classifying, Right Angles & Cutting

A quadrilateral is any shape with four straight sides, and the OC test loves the family relationships inside that group. A rectangle has four right angles. A rhombus has four equal sides. A square has BOTH, so it is a rectangle AND a rhombus at the same time. That is why 'all squares are rectangles' is true but 'all rectangles are squares' is false — being a rectangle is the easier test to pass. A parallelogram just needs both pairs of opposite sides parallel, so rectangles, rhombuses and squares are all parallelograms. A kite is different: its equal sides are next to each other, not opposite.

The official test drew digits out of horizontal and vertical lines and asked for the largest number of right angles you could count by choosing two of them. The skill is systematic marking: every place two lines meet at a square corner is one right angle — and a line meeting the middle of another line makes TWO, one on each side. Mark them with a tiny square as you go, so nothing is counted twice or missed. Then the question usually adds a twist: 'choose two different figures' — so count each figure, then combine the two biggest totals.

A single straight cut turns one shape into two, and the pieces depend on where the line starts and ends. Cutting a pentagon from corner to corner gives a triangle and a quadrilateral. From a corner to the middle of the opposite side gives two quadrilaterals. Slicing across a corner gives a small triangle and — count carefully — a hexagon, because the cut adds a side to the big piece. The official question listed three possible results and asked which could be made; the method is to try drawing each. If you can draw it, it is possible. The cut line becomes a side of both new pieces.

The test's favourite twist on cutting: 'the shape is cut along the dashed lines into four pieces — how many sides do the pieces have in total?' Students who count the original shape's sides, or who count each cut line once, get it wrong. A cut line becomes an edge of every piece it touches, so it is counted once per piece. The safe method is to name each piece — triangle, rectangle, pentagon — write its number of sides, and add. As a check: a side-to-side cut raises the total by 4, a corner-to-corner cut by only 2.

Several OC questions give three numbered statements and five options that combine them — '1 only', '1 and 3 only' and so on. Do not read the options first; they are designed to make every combination look plausible. Instead, judge each statement on its own and write ✓ or ✗ next to it. For an 'all A are B' statement, one counter-example is enough to make it false — a rectangle that is not a kite kills 'all rectangles are kites'. Only when all three are marked do you look for the single option that lists exactly your ticks. Quiz and exercises now!