A line segment AB has length 14 cm. Its perpendicular bisector is constructed. State the distance from the midpoint of AB to point B.
(1)
2
An angle of 130 degrees is bisected using compasses. State the size of each of the two equal angles formed.
(1)
3
A circle has centre O and radius 6 cm. A point P lies on the circle. State the distance OP.
(1)
4
A triangle is to be constructed with AB = 10 cm, angle A = 55 degrees and angle B = 70 degrees, using a ruler and protractor. Work out the size of angle C.
(2)
5
An angle XOY measures 84 degrees. Its bisector OZ is constructed. State the size of angle YOZ.
(1)
6
Triangle DEF has sides DE = 5 cm, EF = 8 cm and DF = 10 cm. State which construction method (SSS, SAS or ASA) is appropriate, and state the compass radius needed to draw the arc from point D marking side DF.
(2)
7
Line segment PQ has length 20 cm. State the length of each half after its perpendicular bisector is constructed.
(1)
8
Line segment PQ is 16 cm long. Its perpendicular bisector meets PQ at M. A point R lies on the perpendicular bisector so that RM = 6 cm. Using Pythagoras' theorem, work out the distance RP.
(2)
9
An equilateral triangle is constructed using compasses with side length 11 cm. Work out its perimeter.
(2)
10
Angle XOY measures 150 degrees. It is bisected, and then the resulting angle is bisected again. Work out the size of the final angle produced.
(2)
11
A circle has centre O and diameter 18 cm. A point P lies on the circle. Work out the distance OP.
(2)
12
A line segment RS has length 30 cm. It is divided by its perpendicular bisector into two equal parts, and then one of those parts is itself bisected. Work out the length of the smallest part produced.
(2)
13
Triangle JKL is constructed with JK = 7 cm, angle J = 48 degrees and angle K = 82 degrees, using ruler and protractor. Work out angle L.
(2)
14
A student constructs triangle ABC with AB = 9 cm, angle A = 42 degrees and angle B = 58 degrees, using a ruler and protractor. Work out angle C, then state which construction method (SSS, SAS or ASA) was used.
(3)
15
A student constructs the perpendicular bisector of segment MN. The endpoints are M(2, 3) and N(10, 9). Work out the coordinates of the midpoint of MN, and the length of MN.
(3)
16
Using compasses, an equilateral triangle PQR with side length 8 cm is constructed. A second point S is added so that triangle PQS is also equilateral with side length 8 cm, sharing side PQ, on the opposite side of PQ from R. Work out the size of angle RPS.
(3)
17
A circle has centre O and radius 7 cm. A chord AB is constructed with length 7 cm. Since OA = OB = AB = 7 cm, state the type of triangle OAB and work out the size of angle AOB.
(3)
18
Triangle JKL is constructed given JL = 9 cm, angle J = 40 degrees and angle L = 65 degrees. Work out angle K, and name which side of the triangle is the longest (in terms of two vertices).
(3)
19
Stretch question. A right-angled triangle is constructed with legs 9 cm and 12 cm meeting at a right angle. Work out the length of the hypotenuse. The perpendicular bisector of the hypotenuse is then constructed; using the fact that this point is equally distant from all three vertices, state the distance from the midpoint of the hypotenuse to each of the three vertices.
(4)
Mark scheme · KS3.M-G6D Measuring, Drawing and Constructing: Fluency and Exam Drill
Question 1
B1 7 cm cao
Answer: 7 cm
Question 2
B1 65 degrees cao
Answer: 65 degrees
Question 3
B1 6 cm cao
Answer: 6 cm
Question 4
M1 uses angle sum of a triangle = 180
A1 55 degrees cao
Answer: 55 degrees
Question 5
B1 42 degrees cao
Answer: 42 degrees
Question 6
B1 SSS (side-side-side)
B1 radius = 10 cm cao
Answer: SSS; radius 10 cm
Question 7
B1 10 cm cao
Answer: 10 cm
Question 8
M1 uses PM = 8 cm and RP2 = 82 + 62
A1 RP = 10 cm cao
Answer: 10 cm
Question 9
M1 uses all three sides equal to 11 cm
A1 33 cm cao
Answer: 33 cm
Question 10
M1 first bisection: 150 / 2 = 75 degrees
A1 second bisection: 37.5 degrees cao
Answer: 37.5 degrees
Question 11
M1 uses radius = diameter / 2
A1 9 cm cao
Answer: 9 cm
Question 12
M1 first bisection: 30 / 2 = 15 cm
A1 second bisection: 7.5 cm cao
Answer: 7.5 cm
Question 13
M1 uses angle sum of a triangle = 180
A1 50 degrees cao
Answer: 50 degrees
Question 14
M1 uses angle sum of a triangle = 180
A1 angle C = 80 degrees cao
B1 ASA (angle-side-angle)
Answer: Angle C = 80 degrees; method ASA
Question 15
M1 uses midpoint = ((2+10)/2, (3+9)/2) = (6, 6)
M1 uses length = √(10-2)2 + (9-3)2
A1 length = 10 cao
Answer: Midpoint (6, 6); length 10
Question 16
M1 recognises each equilateral triangle has a 60 degree angle at P
M1 adds the two 60 degree angles at P across the shared vertex
A1 120 degrees cao
Answer: 120 degrees
Question 17
M1 recognises OA = OB = AB so all three sides are equal