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Arithmetic Ability
Triangles
Quiz 1
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Q.1
In ΔABC and ΔDEF, if ∠A = 50°, ∠B = 70°, ∠C = 60°, ∠D = 60°, ∠E = 70° and ∠F = 50°, then
ΔABC ∼ ΔFED
ΔABC ∼ ΔDFE
ΔABC ∼ ΔEDF
ΔABC ∼ ΔDEF
Q.2
The centroid of a triangle is G. If area of ΔABC = 72 sq. unit, then the area of ΔBGC is?
16 sq. units
24 sq. units
36 sq. units
48 sq. units
Q.3
An equilateral triangle of side 6 cm is inscribed in a circle. Then radius of the circle is:
$$2\sqrt 3 $$ cm
$$3\sqrt 2 $$ cm
$$4\sqrt 3 $$ cm
$$\sqrt 3 $$ cm
Q.4
If ABC and PQR are similar triangles in which ∠A = 47° and ∠Q = 83°, then ∠C is:
50°
70°
60°
80°
Q.5
The orthocenter of a triangle is the point where?
The medians meet
The altitudes meet
The right bisectors of the sides of
The bisectors of the angles
Q.6
Possible length of the sides of a triangle are:
2cm, 3cm, 6cm
3cm, 4cm, 5cm
2.5cm, 3.5cm, 6cm
4cm, 4cm, 9cm
Q.7
Length of the sides of a triangle are a, b and c respectively. If a
2
+ b
2
+ c
2
= ab + bc + ca then the triangle is:
Isosceles
Equilateral
Scalene
Right-angled
Q.8
Three sides of a triangle are 5 cm, 9 cm and x cm. The minimum integral value of x is:
2
3
4
6
Q.9
Which of the set of three sides can't form a triangle?
5cm, 6cm, 7cm
5cm, 8cm, 15cm
8cm, 15cm, 18cm
6cm, 7cm, 11cm
Q.10
In a triangle ABC, if ∠A + ∠C = 140° and ∠A + 3∠B = 180°, then ∠A is equal to:
80°
40°
60°
20°
Q.11
Given that the ratio of altitudes of two triangles is 4 : 5, ratio of their areas is 3 : 2, the ratio of their corresponding bases is :
5 : 8
15 : 8
8 : 5
8 : 15
Q.12
In a ΔABC, If 2∠A = 3∠B = 6∠C, then the value of ∠B is:
60°
30°
45°
90°
Q.13
∠A + $$\frac{1}{2}$$ ∠B + ∠C = 140°, then ∠B is :
50°
80°
40°
60°
Q.14
The equidistant point from the vertices of a triangle is called its:
Centroid
Incenter
Circumcenter
Orthocenter
Q.15
In ΔABC, ∠B = 70° and ∠C = 30°, AD and AE are respectively the perpendicular on side BC and bisector of ∠A. The measure of ∠DAE is:
24°
10°
15°
20°
Q.16
If the three angles of a triangle are: $${\left(x + 15 \right)^ \circ },$$ $${\left({\frac{{6x}}{5} + 6} \right)^ \circ }$$ and $${\left({\frac{{2x}}{3} + 30} \right)^ \circ }$$ then the triangle is:
Isosceles
Equilateral
Right angled
Scalene
Q.17
Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is
AX = BY = CZ
AX ≠ BY = CZ
AX = BY ≠ CZ
AX ≠ BY ≠ CZ
Q.18
In a triangle, if three altitudes are equal, then the triangle is
Obtuse
Equilateral
Right
Isosceles
Q.19
If in a triangle, the orthocentre lies on vertex, then the triangle is
Acute angled
Isosceles
Right angled
Equilateral
Q.20
Taking any three of the line segments out of segments of length 2 cm, 3 cm, 5 cm and 6 cm, the number of triangles that can be formed is:
3
2
1
4
Q.21
If the incentre of an equilateral triangle lies inside the triangle and its radius in 3 cm, then the side of the equilateral triangle is
9$$\sqrt 3 $$ cm
6$$\sqrt 3 $$ cm
3$$\sqrt 3 $$ cm
6 cm
Q.22
If the circumcentre of a triangle lies outside it, then the triangle is
Equilateral
Acute angled
Right angled
Obtuse angled
Q.23
The orthocentre of a right angled triangle lies
Outside the triangle
At the right angular vertex
On its hypotenuse
Within the triangle
Q.24
ABC is an equilateral triangle. Points D, E and F are taken as the mid-point on sides AB, BC, AC respectively, so that AD = BE = CF. Then AE, BF, CD enclosed a triangle which is:
Equilateral
Isosceles triangle
Right angle triangle
None of these
Q.25
In a ΔABC, BC is extended upto D; ∠ACD = 120°, ∠B = $$\frac{1}{2}$$ ∠A, then ∠A is:
60°
75°
80°
90°
Q.26
The side BC of a triangle ABC is proceed to D. If ∠ACD = 112° and ∠B = $$\frac{3}{4}$$ ∠A, then the measure of ∠B is:
64°
30°
48°
45°
Q.27
Let ΔABC and ΔABD be on the same base AB and between the same parallels AB and CD. Then the relation between areas of triangles ABC and ABD will be
ΔABD = $$\frac{1}{3}$$ ΔABC
ΔABD = $$\frac{1}{2}$$ ΔABC
ΔABC = $$\frac{1}{2}$$ ΔABD
ΔABC = ΔABD
Q.28
G is the centroid of ΔABC. If AB = BC = AC, then measure of ∠BGC is:
45°
60°
90°
120°
Q.29
ΔABC is similar to ΔDEF. If the sides of ΔABC, that is AB, BC and CA, are 3, 4 and 5 cms respectively, what would be the perimeter of the ΔDEF, if the side DE measures 12 cms ?
24 cms
30 cms
36 cms
48 cms
Q.30
In ΔABC and ΔPQR, ∠B = ∠Q, ∠C = ∠R. M is the midpoint on QR, If AB : PQ = 7 : 4, then $$\frac{{{\text{area}}\,\left( {\vartriangle ABC} \right)}}{{{\text{area}}\,\left( {\vartriangle PMR} \right)}}$$ is :
$$\frac{{35}}{8}$$
$$\frac{{35}}{{16}}$$
$$\frac{{49}}{{16}}$$
$$\frac{{49}}{8}$$
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