Part A: Numeracy
6
Geometry & Spatial Reasoning
Understand angles, shapes, scale drawings, and coordinates
Learning Objectives
- Calculate unknown angles using parallel line and triangle rules
- Identify properties of 2D and 3D shapes
- Read coordinate grids and describe grid transformations
- Apply scale factors to solve perimeter and area scaling problems
Chapter Progress: 0%
Section 1: Properties of 2D and 3D Shapes
2D shapes have width and length, while 3D shapes add depth. Prisms have uniform cross-sections, whereas pyramids taper to a point (vertex).
2D vs 3D Shapes
| Shape | Type | Properties |
|---|---|---|
| Square | 2D | 4 equal sides, 4 right angles |
| Cube | 3D | 6 square faces, 12 edges, 8 vertices |
| Cylinder | 3D | 2 circular bases, 1 curved surface |
Section 2: Angles & Geometric Rules (triangles, parallel lines)
Understanding angles is crucial. Angles on a straight line add up to 180°. Angles inside a triangle sum to 180°.
Angle Formulas
Example 1
Finding the Missing Angle in a Right-Angled Triangle
❓ Question: In a right-angled triangular ramp structure ABC, angle B is a right angle (90°) and angle A measures 35°. What is the measure of angle C?
📄 Source Passage / Reference Data: Ramp Geometry Specifications: The wheelchair access ramp forms a right-angled triangle ABC where angle B = 90° and angle A = 35°.
📝 Step-by-Step Method:
1
State the fundamental geometric rule for triangle interior angles (Sum = 180°).
2
Sum the two known angles.
3
Subtract the known sum from 180° to isolate Angle C.
🔍 Evidence Extracted: "right-angled triangle ABC where angle B = 90° and angle A = 35°."
🎯 Final Answer: 55°
💡 Why It Is Correct: Since interior angles of any triangle sum to 180°, 180° - (90° + 35°) = 55°.
⚡ LANTITE Exam Strategy: Shortcut: In any right-angled triangle, the two acute angles always sum to 90° (90° - 35° = 55°).
Section 3: Symmetry, Transformations, and Tessellations
Symmetry means a shape looks identical to its original shape after being flipped or turned. Transformations include translation, rotation, and reflection. Tessellations are patterns of shapes that fit together perfectly without any gaps.
Section 4: Reading Grid Maps and Coordinates
Grid maps use a Cartesian coordinate system. The horizontal axis is the x-axis and the vertical axis is the y-axis.
Question 1 of 6
What is the sum of angles in a quadrilateral?