Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Construct a quadrilateral PQRS where PQ = 4 cm, QR = 5 cm, RS = 6 cm, SP = 7 cm, and angle PQR = 90°. Which step correctly begins this construction?
- ADraw PQ = 4 cm, then make a 90° angle at Q and mark QR = 5 cm
- BDraw PQ = 4 cm, then make a 90° angle at P and mark QR = 5 cm
- CDraw QR = 5 cm first, then make a 90° angle at R and mark RS = 6 cm
- DDraw the diagonal PR first, then mark the four sides from it
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Answer: A) Draw PQ = 4 cm, then make a 90° angle at Q and mark QR = 5 cm
Draw PQ = 4 cm. At Q, draw a 90° angle and draw QR = 5 cm. Draw RS = 6 cm and SP = 7 cm to complete the quadrilateral.
2. When constructing a rhombus given one side and one angle, which step should be done FIRST?
- ADraw one side of the given length
- BUse a protractor to draw the given angle at one end
- CDraw the second side of the same length
- DComplete the rhombus by drawing the remaining sides
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Answer: A) Draw one side of the given length
The construction begins by drawing one side of the given length, then drawing the given angle at one end before completing the figure.
3. To construct a parallelogram ABCD, what is the minimum information that is sufficient?
- ATwo adjacent sides and the included angle
- BOnly one side
- COnly one angle
- DOnly one diagonal
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Answer: A) Two adjacent sides and the included angle
Because opposite sides of a parallelogram are equal and parallel, two adjacent sides with the angle between them determine the whole figure.
5. Which statement correctly distinguishes a rhombus from a square?
- AA rhombus need not have right angles, while a square always does
- BA rhombus has unequal sides, while a square has equal sides
- CA rhombus has no parallel sides, while a square has
- DA rhombus has three sides, while a square has four
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Answer: A) A rhombus need not have right angles, while a square always does
Both have four equal sides and parallel opposite sides, but a square must have all angles 90°, whereas a rhombus need not. A square is a special rhombus.