Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. What is the first step in constructing an angle bisector?
- ADraw a line segment.
- BPlace the compass on the vertex and draw an arc.
- CMeasure the angle with a protractor.
- DDraw a perpendicular line.
Show answer
Answer: B) Place the compass on the vertex and draw an arc.
To construct an angle bisector, start by placing the compass on the vertex and drawing an arc that intersects both sides of the angle.
2. What is the significance of constructing triangles accurately in engineering?
- AEnsures structural stability
- BReduces the cost of building materials
- CMakes the structure heavier and stronger
- DRemoves the need for any measurements
Show answer
Answer: A) Ensures structural stability
Accurate triangle construction is crucial in engineering for ensuring structural stability and allowing precise measurements in designs.
3. Which set of three sides CANNOT form a triangle (and so cannot be constructed)?
- A2 cm, 3 cm, 6 cm
- B4 cm, 5 cm, 6 cm
- C3 cm, 4 cm, 5 cm
- D5 cm, 5 cm, 8 cm
Show answer
Answer: A) 2 cm, 3 cm, 6 cm
By the triangle inequality, the sum of two sides must exceed the third. Here 2 + 3 = 5 < 6, so these sides cannot form a triangle.
5. Why can a unique triangle NOT be constructed if only its three angles are given (AAA)?
- ABecause the angles fix only the shape, not the size, so infinitely many similar triangles fit.
- BBecause the angles do not add up to 180 degrees.
- CBecause at least one side must always be a right angle.
- DBecause a compass cannot copy an angle.
Show answer
Answer: A) Because the angles fix only the shape, not the size, so infinitely many similar triangles fit.
Three angles determine the shape (all such triangles are similar) but not the scale. Without at least one side length, infinitely many triangles satisfy the conditions, so the triangle is not unique.