MCQ Questions

Question No. 1

Construct and verify bisector of CD

Answer :

a) Draw a line of 10 cm and label endpoints C and D.

b) Bisect CD.

c) Measure your partner’s lines and confirm each half is 5 cm.

Question No. 2

Construct and verify bisector of JK

Answer :

a) Draw a line of 7 cm and label endpoints J and K.

b) Bisect JK.

c) Measure your partner’s lines and confirm each half is 3.5 cm.

Question No. 3

Construct and verify bisector of ST

Answer :

a) Draw a line of 84 mm and label endpoints S and T.

b) Bisect ST.

c) Measure your partner’s lines and confirm each half is 42 mm.

Question No. 4

Construct and bisect angles in ∠ABC.

Answer :

a) Construct ∠ABC = 90°

b) Bisect ∠ABC to give ∠DBC = 45°

c) Bisect ∠DBC to give ∠EBC = 22.5°

Question No. 5

Use a protractor to measure and label your partner’s angles from question 1.

Answer :

Question No. 6

Construct and bisect angles in ∠PQR.

Answer :

a) Construct ∠PQR = 60°

b) Bisect ∠PQR to give ∠SQR = 30°

c) Bisect ∠SQR to give ∠TQR and measure ∠TQR

Question No. 7

Use a protractor to measure and label your partner’s angles from question 3.

Answer :

Question No. 8

With your partner, discuss the previous example in which an angle of 60° was used to construct an angle of 120°. Explain how you would adapt this idea to construct an angle of 150° or of 135°.

Answer :

Question No. 9

Construct and bisect angles in ∠KLM.

Answer :

a) Construct ∠KLM = 150°

b) Bisect ∠KLM to give ∠NLM

c) Measure ∠NLM

Question No. 10

Use a protractor to measure your partner’s angles in question 2. Make sure that all the angles are labelled correctly and that the measurements are correct.

Answer :

Question No. 11

Construct and bisect angles in ∠QRS.

Answer :

a) Construct ∠QRS = 135°

b) Bisect ∠QRS to give ∠TRS

c) Measure ∠TRS

Question No. 12

Use a protractor to measure your partner’s angles in question 4. Make sure that all the angles are labelled correctly and that the measurements are correct.

Answer :

Question No. 13

Construct △DEF with DE = EF = DF = 7.5 cm.

Answer :

a) Measure ∠D, ∠E and ∠F

b) What kind of triangle is △DEF?

Question No. 14

Construct △ABC with AB = 10 cm, BC = 8 cm and AC = 6 cm.

Answer :

a) Measure ∠A, ∠B and ∠C

b) What kind of triangle is △ABC?

Question No. 15

Construct △RST with ∠R = 135°, RS = 45 mm and RT = 45 mm.

Answer :

a) Measure ∠S, ∠T and ST

b) What kind of triangle is △RST?

Question No. 16

Construct △XYZ with XY = 72 mm, ∠X = 75° and ∠Y = 30°.

Answer :

a) Measure ∠Z, YZ and XZ

b) What kind of triangle is △XYZ?

Question No. 17

Construct two different triangles such that ∠C = 45°, CD = 6 cm and DE = 4.5 cm.

Answer :

a) For each triangle, measure ∠D, ∠E and CE

b) What kind of triangle is each one?

Question No. 18

Construct three different right-angled triangles with angles 90°, 60° and 30° and one side of 6 cm.

Answer :

a) Vary the placement of the 6 cm side to produce three distinct constructions

Question No. 19

Construct ∠DEF = 75° with DE = EF = 7 cm; construct EG = 9 cm as the bisector of ∠DEF; join DG, FG and DF; mark H at EG∩DF; measure DG, FG, DH, FH and ∠DHG; identify quadrilateral DEFG.

Answer :

a) Construct ∠DEF = 75° with DE = EF = 7 cm.

b) Construct EG = 9 cm as the bisector of ∠DEF.

c) Join DG, FG and DF; mark H at EG∩DF.

d) Measure DG and FG.

e) Identify quadrilateral DEFG using side lengths.

f) Measure DH, FH and ∠DHG and explain.

Question No. 20

Construct a circle of radius 4.5 cm; draw two diameters at 30° to one another meeting the circumference at P, Q, R, S; identify quadrilateral PQRS.

Answer :

a) Draw a circle of radius 4.5 cm.

b) Draw two diameters at 30°, meeting the circle at P, Q, R, S.

c) Identify quadrilateral PQRS using measurements.

Question No. 21

Construct parallelogram PQRS with ∠P = 45°, PQ = 5 cm, PS = 8 cm; bisect all angles; let A, B, C, D be intersections of bisectors; identify quadrilateral ABCD.

Answer :

a) Construct PQRS as given.

b) Bisect ∠P, ∠Q, ∠R, ∠S.

c) Mark intersection of adjacent bisectors as A, B, C, D.

d) Identify quadrilateral ABCD using measurements.

Question No. 22

Mark points A, B with AB = 6 cm; draw circles centre A, B radius 5 cm; let C, D = intersections; join AC, BC, BD, AD; identify quadrilateral ACBD.

Answer :

a) Mark A, B 6 cm apart.

b) Draw circles centre A and B, radius 5 cm.

c) Let C, D be intersections; join AC, BC, BD, AD.

d) Identify quadrilateral ACBD using measurements.

Question No. 23

Construct △XYZ with XY = XZ = 7 cm, YZ = 3.5 cm; construct midpoints M of XY and N of XZ; extend MN to P so MN = NP; identify quadrilateral MPZY.

Answer :

a) Construct △XYZ as given.

b) Construct M, N midpoints; extend to P so MN = NP.

c) Identify quadrilateral MPZY using measurements.

Question No. 24

Draw any circle; choose four points A, B, C, D on circumference; join AB, BC, CD, DA; measure ∠A, ∠B, ∠C, ∠D; state sums of ∠A+∠C and ∠B+∠D; conclude about opposite angles.

Answer :

a) Draw circle; mark A, B, C, D on circumference.

b) Join AB, BC, CD, DA.

c) Measure ∠A, ∠B, ∠C, ∠D.

d) Compute ∠A+∠C and ∠B+∠D.

e) Conclude relationship of opposite angles.

Question No. 25

Given a circle with centre C and radius 6 cm. The locus of point P is outside the circle, exactly 2 cm from the circumference.

Answer :

a) Construct circle C and the locus of P (dotted) and show three possible positions of P.

b) Describe the locus of P.

Question No. 26

Given line AB = 4 cm. The locus of point P is exactly 1 cm from line AB.

Answer :

a) Construct line AB and the locus of P (dotted) and show four possible positions of P.

b) Describe the locus of P.

Question No. 27

Construct ∠PQR = 60° with PQ = QR = 6 cm. The locus of point P is equidistant from lines PQ and QR.

Answer :

a) Construct ∠PQR and sides PQ, QR.

b) Construct the locus of P (dotted) and show three possible positions of P.

c) Describe the locus of P.

Question No. 28

Construct any △ABP. The locus of point P is such that the area of △APB remains constant.

Answer :

a) Construct △ABP.

b) Construct the locus of P (dotted) and show three possible positions of P.

c) Describe the locus of P.

Question No. 29

Construct any square ABCD. The locus of point P is within the square and equidistant from vertices A and C.

Answer :

a) Construct square ABCD.

b) Construct the locus of P (dotted) and show three possible positions of P.

c) Describe the locus of P in terms of vertices A and C.

Question No. 30

LM is a horizontal line segment; point N is above LM. Construct and describe the locus of N if △LMN is isosceles (LN = MN), equilateral, and right-angled at L.

Answer :

a) For isosceles (LN=MN), construct LM and locus of N; show possible N.

b) For equilateral, construct locus of N; show possible N.

c) For right-angled at L, construct locus of N; show possible N.

Question No. 31

Construct △XYZ with XY = 6 cm, ∠Y = 135° and YZ = 5 cm; bisect XZ at M; construct a circle centre M, radius 3 cm. The locus of P lies within △XYZ but outside the circle.

Answer :

a) Construct △XYZ and bisect XZ to find M.

b) Draw circle centre M, radius 3 cm.

c) Shade the region(s) within △XYZ but outside the circle to represent the locus of P.

Question No. 32

Given points X and Y. The locus of P is always 4 cm from X; the locus of Q is always 6 cm from Y.

Answer :

a) Describe the loci of P and Q.

b) If the loci touch but do not overlap, determine the distance XY and illustrate.

c) If the loci do not touch or overlap, describe all possible distances XY and illustrate.

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