Q 1 – In the given figure, the measure of ∠BAC is
(a) 60°
(b) 50°
(c) 70°
(d) 80°
Ans. (b) 50°
Q 2 – If AB = QR, BC=RP, and CA = QP, then which of the following holds?
(a) △BCA ≅ △PQR
(b) △ABC ≅ △PQR
(c) △CBA ≅ △PQR
(d) △CAB ≅ △PQR
Ans. (d) △CAB ≅ △PQR
Q 3 – If E and F are the midpoints of equal sides AB and AC of a triangle ABC. Then:
a) BF=AC
b) BF=AF
c) CE=AB
d) BF = CE
Ans. d) BF = CE
Q 4 – In ΔABC, ∠C = ∠A and BC = 6 cm
and AC = 5 cm. Then the length of AB is:
(a) 6 cm
(b) 5 cm
(c) 3 cm
(d) 2.5 cm
Ans. (a) 6 cm
Q 5 – In figure if AE || DC and AB = AC, find the value of ∠ABD.
(a) 130°
(b) 110°
(c) 120°
(d) 70°
Ans. (a) 130°
Q 6 – Which of the following statements is incorrect ?
(a) Two squares having the same side length are congruent
(b) Two rectangles having the same area are congruent
(c) Two circles having the same radius are congruent
(d) Two lines having same length are congruent
Ans. (b) Two rectangles having the same area are congruent
Q 7 – ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Then:
a) BE>CF
b) BE<CF
c) BE=CF
d) None of the above
Ans. c) BE=CF
Q 8 – If the bisector of the angle A of a △ABC is perpendicular to the base BC of the triangle then the triangle ABC is :
(a) Obtuse Angled
(b) Isosceles
(c) Scalene
(d) Equilateral
Ans. (b) Isosceles
Q 9 – In figure X is a point in the interior of square ABCD, AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then find BY.
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Ans. (c) 7 cm
Q 10 – In ΔABC if AB = BC, then :
(a) ∠B > ∠C
(b) ∠A = ∠C
(c) ∠A = ∠B
(d) ∠A < ∠B
Ans. (b) ∠A = ∠C
Q 11 – If two triangles ABC and PQR are congruent under the correspondence A ↔ P, B ↔ Q and C ↔ R, then symbolically, it is
expressed as
(a) ΔABC ≅ ΔPQR
(b) ΔABC = ΔPQR
(c) ΔABC and ΔPQR are scalene triangles
(d) ΔABC and ΔPQR are isosceles triangles
Ans. (a) ΔABC ≅ ΔPQR
Q 12 – In figure AB ⊥ AE, BC ⊥ AB, CE = DE and ∠AED = 120°, then find ∠ECD.
(a) 80°
(b) 70°
(c) 85°
(d) 60°
Ans. (d) 60°
Q 13 – If ABC and DBC are two isosceles triangles on the same base BC. Then:
a) ∠ABD = ∠ACD
b) ∠ABD > ∠ACD
c) ∠ABD < ∠ACD
d) None of the above
Ans. a) ∠ABD = ∠ACD
Q 14 – Two equilateral triangles are congruent when:
(a) Their areas are proportional
(b) Their sides are equal
(c) Their sides are proportional
(d) Their angles are equal
Ans. (b) Their sides are equal
Q 15 – In ΔABC, AB = AC and ∠B = 50°, then find ∠C.
(a) 50°
(b) 40°
(c) 80°
(d) 120°
Ans. (a) 50°
Q 16 – P is a point on side BC of Δ ABC, such that AP bisects ∠BAC, then :
(a) BP = CP
(b) BA > BP
(c) BP > BA
(d) CP < CA
Ans. (b) BA > BP
Q 17 – In figure, ABC is an isosceles triangle whose side AC is produce to E and through C, CD is drawn parallel to BA. Find the value of x.
(a) 52°
(b) 156°
(c) 76°
(d) 104°
Ans. (d) 104°
Q 18 – D is a Point on the Side BC of a △ABC such that AD bisects ∠BAC then:
(a) BD = CD
(b) CD > CA
(c) BD > BA
(d) BA > BD
Ans. (d) BA > BD
Q 19 – If AD is an altitude of an isosceles triangle ABC in which AB = AC. Then:
a) BD=CD
b) BD>CD
c) BD<CD
d) None of the above
Ans. c) BD<CD
Q 20 – In figure AB ⊥ BE and EF ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to
(a) ΔEFC
(b) ΔECF
(c) ΔDEF
(d) ΔFEC
Ans. (d) ΔFEC
Q 21 – ABC ≅ △PQR. If AB=5 cm, and then which of the following is true?
(a) QR = 5 CM, ∠R= 60°
(b) QP = 5 cm, ∠P= 60°
(c) QP = 5cm, ∠R = 60°
(d) QR = 5 CM, ∠Q = 60°
Ans. (b) QP = 5 cm, ∠P= 60°
Q 22 – In a right triangle, the longest side is:
a) Perpendicular
b) Hypotenuse
c) Base
d) None of the above
Ans. b) Hypotenuse
Q 23 – D is a point on the side BC of a ΔABC such that AD bisects ∠BAC. Then
(a) BD = CD
(b) BA > BD
(c) BD > BA
(d) CD > CA
Ans. (b) BA > BD
Q 24 – The angles opposite to equal sides of a triangle are:
(a) Equal
(b) Unequal
(c) supplementary angles
(d) Complementary angles
Ans. (a) Equal
Q 25 – Two sides of a triangle are of lengths 5 cm and 1.5 cm. The length of the third side of the triangle cannot be
(a) 3.6 cm
(b) 4.1 cm
(c) 3.8 cm
(d) 3.4 cm
Ans. (d) 3.4 cm
Q 26 – In ΔPQR, if ∠R > ∠Q, then
(a) QR > PR
(b) PQ > PR
(c) PQ < PR
(d) QR < PR
Ans. (b) PQ > PR
Q 27 – In △ABC, if ∠B = 30∘ and ∠C = 70∘, then which of the following is the longest side?
(a) AB
(b) BC
(c) AC
(d) AB or AC
Ans. (b) BC
Q 28 – In triangles ABC and PQR, AB = AC, ∠C = ∠P and ∠B = ∠Q. The two triangles are
(a) isosceles but not congruent
(b) isosceles and congruent
(c) congruent but not isosceles
(d) neither congruent nor isosceles
Ans. (a) isosceles but not congruent
Q 29 – In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if
(a) BC = EF
(b) AC = DE
(c) AC = EF
(d) BC = DE
Ans. (b) AC = DE