Geometry rewards drawing. Almost every question here is solved by sketching the figure and marking what you know on it.
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Angles are named by size, and pairs of angles are named by what they add to.
📐 Names by size and by pair
| Name | Meaning |
|---|---|
| Acute | less than 90° |
| Right | exactly 90° |
| Obtuse | between 90° and 180° |
| Straight | exactly 180° |
| Reflex | more than 180° |
| Complementary | a pair adding to 90° |
| Supplementary | a pair adding to 180° |
Do not swap these two. Complementary → Corner → 90°. Supplementary → Straight → 180°. The first letters match the picture.
When a line cuts two parallel lines, eight angles appear — but only two different sizes among them.
🛤️ Which pairs are equal
| Pair | Relationship |
|---|---|
| Corresponding | equal — they sit in matching corners (an F shape) |
| Alternate interior | equal — inside, on opposite sides (a Z shape) |
| Vertically opposite | equal — across an X |
| Co-interior | add to 180° (a C or U shape) |
Look for the letters. An F shape means corresponding angles (equal). A Z shape means alternate angles (equal). A C shape means co-interior angles (adding to 180°). Tracing the letter on the figure is faster than recalling the name.
A figure has line symmetry if it folds onto itself, and rotational symmetry if it looks the same after a turn.
🔷 Symmetry of common shapes
| Shape | Lines of symmetry | Order of rotation |
|---|---|---|
| Square | 4 | 4 |
| Rectangle | 2 | 2 |
| Equilateral triangle | 3 | 3 |
| Rhombus | 2 | 2 |
| Regular hexagon | 6 | 6 |
| Circle | infinite | infinite |
| Parallelogram | 0 | 2 |
A parallelogram has no line of symmetry — folding it never matches. But it does have rotational symmetry of order 2, because turning it half a turn gives the same shape. Line and rotational symmetry are different things.
12 questions on angles, lines and symmetry. Draw before you decide. 🍀
