Year 9 Maths — Why constructions work

1.Why must the compass opening stay the same when you swing arcs from each end of a segment?

• a) So each crossing point is equally far from both ends
• b) So the finished line comes out the same length as the segment
• c) So each arc reaches both ends of the segment
• d) So the finished line comes out horizontal

2.Two sides of a triangle are 6 and 9 cm. What is the smallest whole number the third side could be, in centimetres?

3.To bisect an angle you mark equal distances along both arms, then swing equal arcs from those two marks. The two triangles this makes are congruent by which rule?

• a) AAA
• b) ASA
• c) SSA
• d) SSS

4.Why does the line through those two crossing points pass through the mid-point of the segment?

• a) Because both arcs share a centre
• b) Because it is the longest line that can be drawn
• c) Because it is drawn vertically
• d) Every point on it is the same distance from both ends

5.An angle of 60° is bisected, and one of the halves is then bisected again. How big is the smallest angle now, in degrees?

6.Two sides of a triangle differ by 9 cm and the base is 7 cm. The difference of two sides must be less than the third side for the triangle to exist. Can it be built? Answer yes or no.

7.A triangle can be built only if any two of its sides add up to more than the third. Two sides are 6 and 9 cm. What is the largest whole number the third side could be, in centimetres?

8.A triangle is to be built on a base of 8 cm, with the other two sides adding up to 12 cm. What would its perimeter be, in centimetres?