This document provides worked examples for constructing geometric shapes using a ruler, pencil, and compass. It includes three examples of constructing different shapes step-by-step: 1) a triangle with given side lengths and angles, 2) a triangle with a perpendicular line segment, and 3) a trapezoid with given side lengths and angles. The examples show the step-by-step construction of each shape and measure any required lengths or angles.

1. CONSTRUCTION
WORKED EXAMPLES

2. EXAMPLES

3. EXAMPLE 1
• Using a ruler, a pencil and a pair of compasses, construct triangle 𝐸𝐹𝐺, with 𝐸𝐺 =
6𝑐𝑚, < 𝐹𝐸𝐺 = 60° 𝑎𝑛𝑑 < 𝐸𝐺𝐹 = 90°.
• Measure and state the length of 𝐸𝐹.
• Measure and state the size of < 𝐸𝐹𝐺.

4. EXAMPLE 1- SOLUTION
• Using a ruler, a pencil and a pair of compasses, construct triangle 𝐸𝐹𝐺, with 𝐸𝐺 = 6𝑐𝑚, <
𝐹𝐸𝐺 = 60° 𝑎𝑛𝑑 < 𝐸𝐺𝐹 = 90°.
Step 1: Draw the line segment 𝐸𝐺 = 6𝑐𝑚. Step 2: Construct < 𝐹𝐸𝐺 = 60°

5. EXAMPLE 1- SOLUTION CONT’D
• Using a ruler, a pencil and a pair of compasses, construct triangle 𝐸𝐹𝐺, with 𝐸𝐺 = 6𝑐𝑚, <
𝐹𝐸𝐺 = 60° 𝑎𝑛𝑑 < 𝐸𝐺𝐹 = 90°.
Step 3: Construct < 𝐸𝐺𝐹 = 90°.
Step 4: Join the lines to complete the triangle.

6. EXAMPLE 1- SOLUTION CONT’D
Measure and state the length of 𝐸𝐹. Measure and state the size of < 𝐸𝐹𝐺.
𝑬𝑭 = 𝟏𝟐 𝒄𝒎 < 𝑬𝑭𝑮 = 𝟑𝟎°

7. EXAMPLE 2
Using a ruler, a pencil and a pair of compasses, construct
• a triangle 𝑃𝑄𝑅, with 𝑃𝑄 = 8𝑐𝑚, 𝑃𝑅 = 6 𝑐𝑚 𝑎𝑛𝑑 𝑎𝑛𝑔𝑙𝑒 𝑃 = 60°.
• a line segment 𝑅𝑋, which is perpendicular to 𝑃𝑄 and meets 𝑃𝑄 at 𝑋.
• Measure and state the size of < 𝑄𝑅𝑋.

8. EXAMPLE 2- SOLUTION
Using a ruler, a pencil and a pair of compasses, construct
• a triangle 𝑃𝑄𝑅, with 𝑃𝑄 = 8𝑐𝑚, 𝑃𝑅 = 6 𝑐𝑚 𝑎𝑛𝑑 𝑎𝑛𝑔𝑙𝑒 𝑃 = 60°.
Step 1: Draw the line segment 𝑃𝑄 = 8𝑐𝑚. Step 2: Construct 𝑎𝑛𝑔𝑙𝑒 𝑃 = 60°

9. EXAMPLE 2- SOLUTION CONT’D.
Using a ruler, a pencil and a pair of compasses, construct
• a triangle 𝑃𝑄𝑅, with 𝑃𝑄 = 8𝑐𝑚, 𝑃𝑅 = 6 𝑐𝑚 𝑎𝑛𝑑 𝑎𝑛𝑔𝑙𝑒 𝑃 = 60°.
Step 3: Draw the line segment 𝑃𝑅 = 6𝑐𝑚. Step 4: Join 𝑄 to 𝑅 to complete the
triangle.

10. EXAMPLE 2- SOLUTION CONT’D.
Using a ruler, a pencil and a pair of compasses, construct
• a line segment 𝑅𝑋, which is perpendicular Measure and state the size of < 𝑄𝑅𝑋.
to 𝑃𝑄 and meets 𝑃𝑄 at 𝑋.
< 𝑸𝑹𝑿 = 𝟒𝟒°

11. EXAMPLE 3
Using a ruler, a pencil and a pair of compasses, construct
• The trapezium 𝐴𝐵𝐶𝐷, with 𝐴𝐵 = 8𝑐𝑚, 𝐵𝐴𝐷 = 60°, 𝐴𝐷 = 6 𝑐𝑚,
𝐴𝐵𝐶 = 90°, and 𝐴𝐵 parallel to 𝐶𝐷.

12. EXAMPLE 3- SOLUTION
Using a ruler, a pencil and a pair of compasses, construct
• The trapezium 𝐴𝐵𝐶𝐷, with 𝐴𝐵 = 8𝑐𝑚, 𝐵𝐴𝐷 = 60°, 𝐴𝐷 = 6 𝑐𝑚,
𝐴𝐵𝐶 = 90°, and 𝐴𝐵 parallel to 𝐶𝐷.
Step 1: Draw the line segment 𝐴𝐵 = 8𝑐𝑚. Step 2: Construct 𝐵𝐴𝐷 = 60°

13. EXAMPLE 3- SOLUTION CONT’D.
Using a ruler, a pencil and a pair of compasses, construct
• The trapezium 𝐴𝐵𝐶𝐷, with 𝐴𝐵 = 8𝑐𝑚, 𝐵𝐴𝐷 = 60°, 𝐴𝐷 = 6 𝑐𝑚,
𝐴𝐵𝐶 = 90°, and 𝐴𝐵 parallel to 𝐶𝐷.
Step 3: Construct 𝐴𝐵𝐶 = 90° Step 4: Mark off 6 𝑐𝑚 along the ray from point A,
to label point 𝐷.

14. EXAMPLE 3- SOLUTION CONT’D.
Using a ruler, a pencil and a pair of compasses, construct
• The trapezium 𝐴𝐵𝐶𝐷, with 𝐴𝐵 = 8𝑐𝑚, 𝐵𝐴𝐷 = 60°, 𝐴𝐷 = 6 𝑐𝑚,
𝐴𝐵𝐶 = 90°, and 𝐴𝐵 parallel to 𝐶𝐷.
Step 5: Draw line segment 𝐶𝐷, parallel to 𝐴𝐵 to
complete the trapezium.

15. THE END.