Geometrical Terms (Copy)
1.
Define the term vertex. Give an example from a triangle.
2.
Explain the difference between a line and a line segment.
3.
What is meant by the term plane in geometry? Give one example.
4.
State the difference between parallel lines and perpendicular lines. Draw and label each.
5.
Define perpendicular bisector. Construct the perpendicular bisector of a line segment AB of length 8 cm.
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6.
What is meant by a bearing? Give an example using a compass direction.
7.
Classify the following angles: 30°, 120°, 95°, 270°.
8.
Differentiate between interior and exterior angles of a polygon. Illustrate with a hexagon.
9.
What does it mean if two shapes are similar? Give an example with triangles.
10.
What does it mean if two shapes are congruent? How is this different from similarity?
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
Define scale factor in enlargement. If a triangle has sides 3 cm, 4 cm, 5 cm and it is enlarged by scale factor 2, what are the new lengths?
12.
Name the three types of triangles based on sides. Give one property for each.
13.
Define a right-angled triangle. Give an everyday example where it appears.
14.
Name the following quadrilaterals:
(a) All sides equal, all angles 90°.
(b) Opposite sides parallel and equal, but no right angles.
(c) Two pairs of adjacent sides equal.
15.
Give one real-life example of a parallelogram and one of a trapezium.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
What is meant by a regular polygon? Name three examples.
17.
How many sides does a pentagon, hexagon, octagon, and decagon have?
18.
State the difference between a regular hexagon and an irregular hexagon.
19.
What is the formula for the sum of interior angles of a polygon with n sides? Find the sum for a decagon.
20.
Define the following terms for a circle: centre, radius, diameter, circumference.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
What is a chord of a circle? Draw and label one.
22.
Differentiate between a major arc and a minor arc.
23.
Define a sector of a circle. How is it different from a segment?
24.
Explain what a tangent to a circle is. State its key property.
25.
Classify each solid as 2D or 3D: cube, cone, rectangle, sphere, pyramid.
26.
Give one property of a cube and one of a cuboid.
27.
What is the difference between a prism and a pyramid?
28.
Define a frustum. Give a real-life example.
29.
List the terms face, edge, vertex and apply them to a triangular prism.
30.
Identify whether each is flat (2D surface) or curved (3D surface):
(a) Cone
(b) Sphere
(c) Cylinder
(d) Cube
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
1.
Vertex: A corner point where two or more lines/edges meet.
Example: A triangle has 3 vertices, such as A, B, and C in â–³ABC.
2.
- Line: Extends infinitely in both directions.
- Line segment: Has two endpoints, finite length.
Example: AB is a segment, line AB continues forever.
3.
Plane: A flat surface extending infinitely in all directions. Example: A sheet of paper is a finite portion of a plane.
4.
- Parallel lines: Always the same distance apart, never meet (e.g. railway tracks).
- Perpendicular lines: Meet at 90°.
5.
Perpendicular bisector: A line dividing another into two equal halves at 90°.
Construction: Midpoint of AB (8 cm) = 4 cm, draw perpendicular at midpoint.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
Bearing: A direction measured clockwise from north, given as 3 digits.
Example: East is 090°, South-East is 135°.
7.
30° = acute, 120° = obtuse, 95° = obtuse, 270° = reflex.
8.
- Interior angle: Inside polygon, between sides.
- Exterior angle: Outside, between side and extension.
Example: Hexagon has interior angle of 120°, exterior angle of 60°.
9.
Similar shapes: Same shape, proportional sides, equal angles.
Example: â–³ABC ~ â–³DEF with sides 2:3 ratio.
10.
Congruent shapes: Same size and shape, equal sides and angles.
Different from similarity: congruence requires equal size, similarity does not.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
Scale factor: Multiplier applied to all dimensions.
Triangle with 3,4,5 enlarged by 2 → 6,8,10.
12.
- Equilateral: All sides equal, all angles 60°.
- Isosceles: Two sides equal, base angles equal.
- Scalene: All sides unequal.
13.
Right-angled triangle: Has one 90° angle.
Example: A ladder against a wall forms a right-angled triangle.
14.
(a) Square.
(b) Parallelogram.
(c) Kite.
15.
- Parallelogram: Rhombus-shaped tiles.
- Trapezium: Bridge support structure.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
Regular polygon: All sides and angles equal.
Examples: Equilateral triangle, square, regular hexagon.
17.
Pentagon = 5 sides, hexagon = 6, octagon = 8, decagon = 10.
18.
- Regular hexagon: All 6 sides equal, angles 120°.
- Irregular hexagon: Unequal sides or angles.
19.
Sum = (n – 2) × 180°.
For decagon, (10 – 2) × 180 = 1440°.
20.
- Centre: Point equidistant from all points on circle.
- Radius: Distance from centre to edge.
- Diameter: Twice radius, passes through centre.
- Circumference: Distance around circle.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
Chord: Line joining two points on a circle, not passing through centre (e.g. AB).
22.
- Minor arc: Less than half of circle.
- Major arc: More than half.
23.
Sector: Region enclosed by two radii and an arc.
Segment: Region enclosed by a chord and an arc.
24.
Tangent: A line touching a circle at exactly one point.
Property: Perpendicular to radius at point of contact.
25.
- Cube (3D), Cone (3D), Rectangle (2D), Sphere (3D), Pyramid (3D).
26.
- Cube: All edges equal, all angles 90°.
- Cuboid: Opposite edges equal, angles 90°, not all edges equal.
27.
- Prism: Two identical parallel faces, sides are rectangles.
- Pyramid: One base, all other faces triangular, meet at vertex.
28.
Frustum: A cone or pyramid cut parallel to base.
Example: Bucket, lampshade.
29.
Triangular prism:
- Faces = 5 (2 triangular, 3 rectangular).
- Edges = 9.
- Vertices = 6.
30.
(a) Cone = flat + curved.
(b) Sphere = curved only.
(c) Cylinder = flat + curved.
(d) Cube = flat only.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course