Shapes and Patterns — Important Questions

Regular triangles, Squares, Regular hexagons

Regular triangles (6 × 60° = 360°), squares (4 × 90° = 360°), and hexagons (3 × 120° = 360°) can tessellate because their angles fit perfectly around a point. Pentagons and octagons cannot tessellate alone.

Two sides, Two angles

An isosceles triangle has exactly two equal sides and two equal angles (the base angles). The angles opposite to the equal sides are equal. It's not equilateral (all sides equal).

Adjacent sides

In a kite, two pairs of adjacent (touching) sides are equal. For example, if sides are numbered 1,2,3,4 going around, then side 1 = side 2 and side 3 = side 4. This is different from parallelograms where opposite sides are equal.

3

Each angle of a regular hexagon is 120°. Around a point, angles must sum to 360°. So 360° ÷ 120° = 3 hexagons can fit around a point. This is why hexagons tessellate perfectly, like in honeycombs.