Class 8 Notes - Constructions

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Constructions

In this chapter, students will learn how to accurately draw geometric figures using a ruler, compass, and protractor. Constructions are a fundamental part of geometry and help in understanding the properties of shapes and their relationships.

1. Basic Tools for Constructions

  • Ruler: For drawing straight lines and measuring lengths.
  • Compass: For drawing arcs and circles, and for transferring distances.
  • Protractor: For measuring and constructing angles.
  • Pencil and Eraser: For neat and accurate drawings.

2. Constructing a Line Segment of Given Length

  1. Draw a straight line using a ruler.
  2. Mark a point A on the line.
  3. Place the zero mark of the ruler at A and mark point B at the required length.
  4. Label the segment as AB.

3. Constructing an Angle of Given Measure

  1. Draw a base line and mark a point A on it.
  2. Place the center of the protractor at A and align the base line with the zero line of the protractor.
  3. Mark the required angle (e.g., 60°) and draw a ray from A through this mark.
  4. Label the angle.

4. Constructing a Perpendicular Bisector of a Line Segment

  1. Draw a line segment AB.
  2. With A as center and radius more than half of AB, draw arcs above and below the line.
  3. With B as center and the same radius, draw arcs to intersect the previous arcs.
  4. Join the points of intersection. This line is the perpendicular bisector of AB.

5. Constructing the Angle Bisector

  1. Draw an angle ∠ABC.
  2. With B as center, draw an arc cutting both arms of the angle at P and Q.
  3. With P and Q as centers and equal radius, draw arcs to intersect at R inside the angle.
  4. Draw a ray from B through R. This is the angle bisector.

6. Constructing Triangles

  • SSS (Side-Side-Side): Given all three sides.
  • SAS (Side-Angle-Side): Given two sides and the included angle.
  • ASA (Angle-Side-Angle): Given two angles and the included side.

Steps involve drawing the base, constructing angles or arcs as required, and joining points to complete the triangle.

7. Practical Applications

  • Drawing perpendiculars and parallels in real-life layouts (e.g., maps, buildings).
  • Constructing geometric shapes for art and design.
  • Understanding geometric proofs and properties through constructions.

8. Common Mistakes

  • Not keeping the compass radius fixed while drawing arcs.
  • Misreading the protractor scale.
  • Not labeling points clearly.
  • Using a blunt pencil, leading to inaccurate constructions.

9. Practice Exercises

  1. Construct a triangle with sides 5 cm, 6 cm, and 7 cm.
  2. Draw a line segment of 8 cm and construct its perpendicular bisector.
  3. Construct an angle of 75° and bisect it.
  4. Draw a triangle with angles 60°, 70°, and 50° and one side of 6 cm.

10. Summary

  • Constructions require accuracy and understanding of geometric principles.
  • Always use sharp pencils and proper tools.
  • Label all points and steps clearly.
  • Practice helps in mastering geometric constructions.