Stage 8 - Q1 - 2 marks
Can these lengths form a triangle? Give a reason.
Hint
Start with a known side; use the correct radius and centre for each arc.
Stage 8 - Q2 - 2 marks
Can these lengths form a triangle? Give a reason.
Hint
Start with a known side; use the correct radius and centre for each arc.
Stage 8 - Q3 - 3 marks
A right triangle has hypotenuse 10 cm and a leg of 8 cm. State the construction type and explain which arc to draw.
Hint
Start with a known side; use the correct radius and centre for each arc.
Stage 8 - Q4 - 3 marks
A right triangle has hypotenuse 9 cm and a leg of 7 cm. State the construction type and explain which arc to draw.
Hint
Start with a known side; use the correct radius and centre for each arc.
Stage 8 - Q5 - 4 marks
On separate plain paper, construct triangle ABC with \(AB=5.5\) cm, \(AC=4.3\) cm and \(BC=6.2\) cm. Measure the largest angle.
Hint
Start with a known side; use the correct radius and centre for each arc.
Stage 8 - Q6 - 4 marks
On separate plain paper, construct triangle ABC with \(AB=5.2\) cm, \(AC=4.5\) cm and \(BC=6.2\) cm. Measure the largest angle.
Hint
Start with a known side; use the correct radius and centre for each arc.
Stage 8 - Q7 - 5 marks
List all possible integer third sides for a triangle whose other sides are 4 cm and 7 cm.
Hint
Use both parts of the triangle inequality.
Stage 8 - Q8 - 5 marks
A right triangle is described as having hypotenuse 6 cm and a leg 8 cm. Explain why no construction is possible.
Hint
Compare the given hypotenuse with the known leg.
Stage 8 - Q9 - 5 marks
Two sides of a triangle are 5 cm and 8 cm. The third side is an integer, the perimeter is even, and the triangle is not isosceles. Find every possible third side.
Hint
Combine the geometric, parity and unequal-side conditions.
Stage 8 - Q10 - 5 marks
A right triangle has two known side lengths 6 cm and 10 cm, but the hypotenuse is not identified. Use constructions to show that two different third-side lengths are possible. Measure both to the nearest millimetre.
Hint
Consider separately whether the larger known side is the hypotenuse or a leg.