Angles and Constructions | Year 7 Mathematics (Cambridge) PDF Download

Measuring Angles

Definition

• An angle is formed when two rays or lines meet at a common endpoint, called the vertex.
• Angles are measured in degrees (°).

Types of Angles

• Acute Angle: Measures less than 90°.
• Right Angle: Exactly 90°.
• Obtuse Angle: Between 90° and 180°.
• Straight Angle: Exactly 180°.
• Reflex Angle: Between 180° and 360°.

Measuring Angles

• Use a protractor to measure angles accurately.
• Place the center of the protractor at the vertex of the angle.
• Read the number where the second ray crosses the protractor scale.

Constructing Angles and Shapes

Constructing Angles

• Using a Protractor:
  • Place the protractor on a straight line (baseline).
  • Measure the desired angle and mark it.
• Using Compass and Ruler:
  • Constructing a Right Angle:
    • Start with a line segment using a ruler.
    • Use a compass to draw a perpendicular line at the endpoint of the segment.

Constructing Shapes

• Triangles:
  • Equilateral Triangle: All sides are equal in length.
  • Isosceles Triangle: At least two sides are equal.
  • Scalene Triangle: All sides have different lengths.
• Quadrilaterals:
  • Square: All sides are equal, and all angles are right angles (90°).
  • Rectangle: Opposite sides are equal, and all angles are right angles (90°).
  • Parallelogram: Opposite sides are equal and parallel.

Examples

• Measuring an Angle: Measure the angle formed by the hands of a clock at 3:00.
• Constructing a Right Angle: Draw a corner of a book using a protractor to measure and ensure the angle is 90°.

Summary

Understanding angles involves measuring and constructing them accurately using tools like protractors and compasses. Shapes like triangles and quadrilaterals can be constructed based on specific angle measurements and side lengths, allowing for precise geometric constructions. Learning these skills helps in visualizing and manipulating shapes and angles in various contexts.