CBSE Class 9 Maths Constructions MCQs

Question. The construction of a ΔLMN in which LM = 8 cm, ∠L = 45° is possible when (MN + LN) is _____ .
(A) 6 cm
(B) 7 cm
(C) 9 cm
(D) 5 cm'
Answer : C

Question. Which of the following options is INCORRECT?
(A) An angle of 52.5° can be constructed.
(B) A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm.
(C) A triangle ABC can be constructed in which BC = 6 cm, ∠C = 30° and AC – AB = 4 cm.
(D) A triangle ABC can be constructed in which ∠B = 60°, ∠C = 45° and AB + BC + AC = 12 cm.
Answer : B

Question. Let ABC be a triangle in which BC = 5 cm, ∠B = 60º and AC + AB = 7.5 cm. Given below are the steps of constructing the triangle ABC. Which of the following steps is INCORRECT?
Step I : Draw a line segment BC of length 5 cm.
Step II : Draw an ∠XBC = 60° at point B of line segment BC.
Step III : Cut off PB = 3.5 cm on the ray BX.
Step IV : Join PC.
Step V : Draw ⊥ bisector of BC which intersect ray BX at A. Join AC.
Step VI : ABC is the required triangle.
(A) Step II only
(B) Step III only
(C) Step II and V
(D) Step III and V
Answer : D

Question. Which of the following angles CANNOT be constructed by using ruler and compass only?
(A) 30°
(B) 45°
(C) 70°
(D) 90°
Answer : C

Question. The construction of a ΔABC in which BC = 6 cm and ∠B = 50º is NOT possible when (AB – AC) is equal to _____ .
(A) 5.6 cm
(B) 5 cm
(C) 6 cm
(D) 4.8 cm
Answer : C

Question. Following are the steps of construction of a rectangle ABCD whose adjacent sides are
of lengths 5 cm and 3.5 cm. Arrange them and select the CORRECT option.
(P) Draw a line segment BC of length 5 cm.
(Q) With A as centre, draw an arc of radius 5 cm.
(R) Draw an ∠XBC = 90º at point B of line segment BC.
(S) Cut a line segment AB = 3.5 cm on BX
(T) With C as centre, draw an arc of radius 3.5 cm which intersects the arc at D.
(U) Join AD and CD.
(A) (P) → (S) → (Q) → (R) → (U) → (T)
(B) (P) → (R) → (S) → (Q) → (T) → (U)
(C) (P) → (S) → (R) → (Q) → (T) → (U)
(D) (P) → (Q) → (R) → (S) → (U) → (T)
Answer : B

Question. Following are the steps of construction of a DABC in which AB = 5 cm, ∠A = 30º and AC – BC = 2.5 cm. Arrange them and select the CORRECT option.
(i) Draw ∠BAX = 30º
(ii) Draw the perpendicular bisector of BD which cuts AX at C.
(iii) Draw AB = 5 cm
(iv) Join BD
(v) Join BC to obtain the required triangle ABC
(vi) From ray AX, cut off line segment AD = AC – BC = 2.5 cm
(A) (i) → (iii) → (iv) → (v) → (vi) → (ii)
(B) (iii) → (i) → (vi) → (iv) → (ii) → (v)
(C) (iii) → (i) → (ii) → (v) → (iv) → (vi)
(D) (iii) → (ii) → (iv) → (i) → (vi) → (v)
Answer : B

Question. State 'T' for true and 'F' for false.
(i) A triangle whose sides measure 8 cm, 4 cm and 12 cm can be possible.
(ii) It is possible to construct an angle of 67.5° using ruler and compass only.
(iii) It is possible to construct a DXYZ in which ∠X = 60°, ∠Y = 100° and ∠Z = 20°.
     (i)      (ii)      (iii)
(A) T        F         T
(B) F        F         F
(C) F        T         T
(D) T        T          F
Answer : B

Question. For which of the following conditions the construction of a triangle is NOT possible?
(A) If two sides and one angle is given.
(B) If two sides and included angle between them is given.
(C) If three sides are given.
(D) If two angles and side between them is given.'
Answer : A

Question. Step I & Step V are in correct order while constructing an equilateral triangle one of
whose altitudes measures 5 cm. Which of the following options is CORRECT while arranging the remaining steps in CORRECT order?
Step I : Draw a line XY.
(i) From ∠P, set off PA = 5 cm, cutting PQ at A.
(ii) From P, draw PQ ⊥ XY.
(iii) Mark any point P an XY.
Step V : Construct ∠PAB = 30º and ∠PAC = 30º, meeting XY at B and C respectively.
(A) (i) → (ii) → (iii)
(B) (iii) → (ii) → (i)
(C) (ii) → (i) → (iii)
(D) (iii) → (i) → (ii)
Answer : B

Question. In a pair of set, squares, one if with angles are
(a) 30⁰, 60⁰, 90⁰
(b) 30⁰, 30⁰, 45⁰
(c) 75⁰, 25⁰, 80⁰
(d) 65⁰, 15⁰, 100⁰

Question. In a pair of set, squares, the other is with angles
(a) 45⁰, 45⁰, 90⁰
(b) 30⁰, 50⁰, 100⁰
(c) 60^0, 60⁰, 60⁰
(d) none of these

Question. To draw the perpendicular bisector of line segment AB, we open the compass
(a) more than 1/2 AB
(b) less than 1/2 AB 
(c) equal to  1/2 AB
(d) none of these

Question. To construct an angle of 22 1/2º , we
(a) bisect an angle of 60⁰
(b) bisect an angle of 30⁰
(c) bisect an angle of 45⁰
(d) none of these

Question. To construct a triangle we must know at least its ______ parts.
(a) two
(b) three
(c) one
(d) five

Question. For which of the following condition the construction of a triangle is not possible:
(a) If two sides and angle included between them is not given
(b) If two sides and angle included between them is not given
(c) If its three sides are given
(d) If two angles and side included between them is given

Question. Construction of a triangle is not possible if:
(a) AB + BC < AC
(b) AB + BC = AC
(c) both (a) and (b)
(d) AB + BC > AC

Question. With the help of ruler and compass it is not possible to construct an angle of
(a) 37.5⁰
(b) 40.5⁰
(c) 22.5⁰
(d) 67.5⁰

Question. The construction of a triangle ABC given that BC = 3 cm, 0 is possible when difference of AB and AC is equal to
(a) 3.2 cm
(b) 3.1 cm
(c) 3 cm
(d) 2.8 cm

Question. The construction of a triangle ABC, given that BC = 6cm, < = 45⁰ is not possible when the difference of AB and AC is equal to
(a) 6.9 cm
(b) 5.2 cm
(c) 5.0 cm
(d) 4.0 cm.

Question. Construction of a triangle is not possible if:
(a) AB – BC < AC
(b) AB – BC = AC
(c) both (a) and (b)
(d) AB – BC > AC

Question. To construct an angle of 15⁰, we
(a) bisect an angle of 60⁰
(b) bisect an angle of 30⁰
(c) bisect an angle of 45⁰
(d) none of these