Geometry begins with a question about a particular shape. Before reaching for a formula, decide whether you need an angle, a length, an area, or the name of a segment. Read the labels and the written conditions together. A picture can orient you, while the stated relationships determine the calculation.
Separate a condition supplied by the question from an impression produced by the drawing. A line that looks longest is not automatically a diameter, and a sloping edge is not automatically a height. Once you choose an answer, trace every number or property back to the place where it was given.
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Use a name as a set of conditions
A diameter joins two points on a circle and passes through its centre. In the circle example, check both requirements for each proposed segment. A radius has one endpoint at the centre and the other on the circumference. These endpoint descriptions still apply if the whole drawing is rotated.
Match the calculation to the measurement
For a triangle with angles of 50° and 60°, subtract those two values from the 180° interior-angle total. The result is the third angle, rather than an extra measurement inferred from the sketch. State which angle the subtraction represents.
For the parallelogram example, pair the 6 cm base with its 4 cm perpendicular height. Cutting and moving a triangular end gives a rectangle with the same area, so the area is 6 × 4 = 24 cm². The 5 cm sloping side supplies a different length. Keep square centimetres attached to the result because you have measured area.
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Example 1 · Geometry
A circle has centre O, and A, B and C lie on its circumference. Segment AB passes through O. Which segment is a diameter?
A circle with centre O. A and B are the left and right points on the circumference; AB passes through O. C is the top point on the circumference, joined to O.
AB
OB
OC
OA
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Answer: AB
A diameter joins two points on the circumference and passes through the centre. AB meets both conditions. OA, OB and OC each run only from the centre to the circumference and are radii.
Per-ID original mathematical derivations and faithful English adaptations for 300 existing families, plus original fictional data and diagram conditions. Supports mathematical reasoning, not external facts or independent review approval.
Source checked: 2026-10-04 · Original authoring and derivation record
Example 2 · Geometry
Two angles of a triangle are 50° and 60°. What is its remaining angle?
70°
110°
130°
80°
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Answer: 70°
The angles of a triangle sum to 180°, so the remaining angle is 180 − 50 − 60 = 70°.
Per-ID original mathematical derivations and faithful English adaptations for 300 existing families, plus original fictional data and diagram conditions. Supports mathematical reasoning, not external facts or independent review approval.
Source checked: 2026-10-04 · Original authoring and derivation record
Example 3 · Geometry
A parallelogram has base 6 cm, perpendicular height 4 cm and sloping side 5 cm. What is its area?
20 cm²
15 cm²
24 cm²
30 cm²
Read the answer and explanation
Answer: 24 cm²
Rearranging a triangular end gives a rectangle with base 6 and height 4. The area is 6 × 4 = 24 cm². The sloping side is not the height.
Per-ID original mathematical derivations and faithful English adaptations for 300 existing families, plus original fictional data and diagram conditions. Supports mathematical reasoning, not external facts or independent review approval.
Source checked: 2026-10-04 · Original authoring and derivation record
Topics: Geometry. Range: Everyday knowledge, Broader knowledge. Difficulty: Basic, Standard. These are selected initially. You can change these on the setup screen.
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