EXPLORING 2D SHAPES SHEET 5 UK - Always, Sometimes or Never True? - Reasoning

Oct 22, 2026

Uploaded by Logic

A worksheet on 2D geometry asks students to judge six statements as always true, sometimes true, or never true, and to justify each decision with drawing or written reasoning. The statements focus on properties of trapeziums, circles, parallelograms, kites, and triangles, including angles, symmetry, and relationships between radius and diameter. An answer section provides model classifications and brief explanations, supported by angle equality and symmetry arguments.

LanguageEnglish

CategoryExam

FormatPDF

Pages2

Reading Time5 min

AccessFree to download

ALWAYS, SOMETIMES OR NEVER TRUE?

Statements 1–6

Answers and reasoning

Name Date EXPLORING 2D SHAPES SHEET 5 UK ALWAYS, SOMETIMES OR NEVER TRUE? For each of the statements below, tick whether they are always true, sometimes true or never true. Can you explain your reasoning by drawing or writing? | | STATEMENT | ALWAYS, SOMETIMES OR NEVER TRUE? | REASONING | | --- | --- | --- | --- | | 1) | A trapezium has exactly one right angle. | ALWAYS SOMETIMES NEVER | | | 2) | The radius of a circle is half the diameter. | ALWAYS SOMETIMES NEVER | | | 3) | The opposite angles of a parallelogram are equal. | ALWAYS SOMETIMES NEVER | | | 4) | A kite has a line of symmetry. | ALWAYS SOMETIMES NEVER | | | 5) | A triangle has exactly two mirror lines. | ALWAYS SOMETIMES NEVER | | | 6) | A parallelogram has exactly two lines of symmetry. | ALWAYS SOMETIMES NEVER | | Name Date EXPLORING 2D SHAPES SHEET 5 UK ANSWERS ALWAYS, SOMETIMES OR NEVER TRUE? | | STATEMENT | ALWAYS, SOMETIMES OR NEVER TRUE? | REASONING | | | | | --- | --- | --- | --- | --- | --- | --- | | 1) | A trapezium has exactly one right angle. | ALWAYS SOMETIMES
NEVER | A trapezium either has none, two or four right angles. (*) | | | | | | | | | | | | | 2) | The diameter of a circle is half the radius. | ALWAYS SOMETIMES
NEVER | The radius of a circle is always equal to half the diameter, not the other way round! | | | | | 3) | The opposite angles of a parallelogram are equal. | ALWAYS
SOMETIMES NEVER | This is always true.
| | | Equal angles:
The red angles are equal. The blue angles are equal. | | 4) | A kite has a line of symmetry. | ALWAYS
SOMETIMES NEVER | All kites have at least one line of | | | | | | | | symmetry. | | | | | 5) | A triangle has exactly two mirror lines. | ALWAYS SOMETIMES
NEVER | A triangle can have none, one or three lines of symmetry but never two! | | | | | 6) | A parallelogram has exactly two lines of symmetry. | ALWAYS
SOMETIMES
NEVER | Parallelograms can have 0, 2 or 4 lines of symmetry. This rectangle, which is a parallelogram, has two.
| | | | (*) Most mathematicians define a trapezium as have at least one pair of parallel lines (therefore including squares, rectangles, parallelograms, [etc. as](etc. as) special cases of a trapezium) .

FAQs

How should students handle each statement in this worksheet?

For each statement, students tick whether it is always true, sometimes true, or never true, then explain the reasoning using drawings or written work.

What geometric topics are covered by the six statements?

The statements cover trapeziums, circles, parallelograms, kites, and triangles, focusing on right angles, radius/diameter relationships, equal opposite angles, and lines of symmetry.

What example reasoning is given for the circle radius and diameter claim?

The answers explain that the radius of a circle is always half the diameter, so the classification follows that relationship rather than the reverse.

Oct 22, 2026

Uploaded by Logic