Angles, Lines and Symmetry: Grade 4 Study Guide
Geometry in Grade 4 gives precise names to the shapes and angles we see all around us.
A point is an exact location. A line goes on forever in both directions, a line segment has two endpoints and a ray has one endpoint and goes on forever in one direction. Two lines can be parallel (never meet) or perpendicular (meet at a right angle).
An angle is formed where two rays meet at a point called the vertex. Angles are measured in degrees. A full turn is 360°, a half turn is 180° and a quarter turn is a right angle of 90°.
Types of angles
| Type | Size | Example |
|---|---|---|
| Acute | less than 90° | a slice of pizza |
| Right | exactly 90° | corner of a page |
| Obtuse | between 90° and 180° | a laptop opened wide |
| Straight | exactly 180° | a flat line |
Using a protractor
Place the center of the protractor on the vertex and line up one ray with the 0° mark. Read the number where the other ray crosses the scale. Use the scale that starts at 0 on the ray you aligned. Decide first whether the angle is acute or obtuse, to avoid reading the wrong scale.
Put the midpoint on the vertex.
One ray on 0°.
Where the second ray crosses.
Is the answer sensible for acute or obtuse?
Classifying shapes and symmetry
Triangles can be classified by their sides (equilateral, isosceles, scalene) or angles (acute, right, obtuse). Quadrilaterals include squares, rectangles, parallelograms, rhombuses and trapezoids. A shape has a line of symmetry if it can be folded so both halves match exactly. A square has four, a rectangle two and a scalene triangle none.
Worked examples and common mistakes
Example: A 120° angle is obtuse. Example: Two angles on a straight line: if one is 70°, the other is 180° − 70° = 110°. Angle measures add: a 90° angle split into 35° and an unknown gives 55°. Common mistakes: reading the wrong protractor scale, thinking longer rays make a bigger angle and counting diagonals as lines of symmetry in a non-square rectangle.
Check your understanding: model answers
1. Acute. 2. 180° − 65° = 115°. 3. Four.
✨ Key Takeaways
- Lines, rays and segments have different endpoints.
- Right = 90°, acute < 90°, obtuse > 90°.
- Angles add up when parts are joined.
- Symmetry means both halves match.
💬 Questions for Discussion & Reflection
- What kind of angle is 45°?
- A straight line is split into 65° and another angle. Find it.
- How many lines of symmetry does a square have?
Print graph paper for drawing shapes →