1. How many degrees are in a triangle’s interior angles?
- 360°
- 180°
- 90°
Check the answer and reasoning
180°
A Euclidean triangle has an interior angle sum of 180°.
MATH / IGCSE
Geometry, constructions and mensuration
Angle rules, similarity and congruence justify geometric relationships. Circle theorems connect angles at centres, circumferences, tangents and cyclic quadrilaterals.
Learning objectives
- Explain geometry, constructions and mensuration using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Angle rules, similarity and congruence justify geometric relationships. Circle theorems connect angles at centres, circumferences, tangents and cyclic quadrilaterals.
Perimeter measures boundary length, area measures surface and volume measures space. Similar shapes scale lengths by k, areas by k² and volumes by k³; units must match the quantity.
Equations and relationships
Volume of a circular cylinder.
Worked example
Find the volume of a cylinder with radius 2 cm and height 5 cm.
Follow the solution
Use π × 2² × 5 = 20π cm³.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. Find the volume of a cylinder with radius 2 cm and height 5 cm.
- 10π cm³
- 20π cm²
- 20π cm³
Check the answer and reasoning
20π cm³
Use π × 2² × 5 = 20π cm³.
3. Similar solids have length scale factor 3. What is the volume factor?
- 27
- 3
- 9
Check the answer and reasoning
27
Three independent length dimensions each scale by 3, producing 3³ = 27.