17.3 Constructions with ruler and compasses — Practise
Work independently, then check your answers and reasoning.
- A segment is 10 cm long. How far is its midpoint from either endpoint?
- What angle does a perpendicular make with a line?
- An angle is 74 degrees. What is each angle after bisecting it?
- A compass construction makes an equilateral triangle. State each interior angle.
- For a perpendicular bisector construction, should the compass radius be greater or less than half the segment?
- Two points are both 7 cm from A and B. What locus contains them?
- Two endpoints are 8 cm apart. The crossing point of equal arcs is 3 cm from each endpoint. Is this possible?
- An angle of 96 degrees is bisected. Work out the two resulting angles.
Answers and concise solutions
1. A segment is 10 cm long. How far is its midpoint from either endpoint?
Answer: 5 cm
2. What angle does a perpendicular make with a line?
Answer: 90 degrees
3. An angle is 74 degrees. What is each angle after bisecting it?
Answer: 37 degrees
4. A compass construction makes an equilateral triangle. State each interior angle.
Answer: 60 degrees
5. For a perpendicular bisector construction, should the compass radius be greater or less than half the segment?
Answer: Greater than half
6. Two points are both 7 cm from A and B. What locus contains them?
Answer: The perpendicular bisector of AB
7. Two endpoints are 8 cm apart. The crossing point of equal arcs is 3 cm from each endpoint. Is this possible?
Answer: No; equal radius must exceed 4 cm to cross off the segment.
8. An angle of 96 degrees is bisected. Work out the two resulting angles.
Answer: 48 degrees each