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Arithmetic Ability
Triangles
Quiz 3
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Q.1
In ΔPQR, S and T are point on sides PR and PQ respectively such that ∠PQR = ∠PST, If PT = 5 cm, PS = 3 cm and TQ = 3 cm, then length of SR is
5 cm
6 cm
$$\frac{{31}}{3}$$ cm
$$\frac{{41}}{3}$$ cm
Q.2
ABC is an equilateral triangle and CD is the internal bisector of ∠C. If DC is produced to E such that AC = CE, then ∠CAE is equal to
45°
75°
30°
15°
Q.3
If each angle of a triangle is less than the sum of the other two, then the triangle is
Obtuse angled
Acute or equilateral
Acute angled
Equilateral
Q.4
In ΔABC, two points D and E are taken on the lines AB and BC respectively in such a way that AC is parallel to DE. Then ΔABC and ΔDBE are :
Similar only if D lies outside the line segment AB
Congruent only If D lies out side the line segment AB
Always similar
Always congruent
Q.5
In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD = 111° and ∠ACB = 80°, then the measure of ∠ABC is:
31°
33°
35°
29°
Q.6
In a ΔABC, AB = AC and BA is produced to D such that AC = AD. Then the ∠BCD is :
100°
60°
80°
90°
Q.7
In ΔABC and ΔDEF, AB = DE and BC = EF, then one can infer that ΔABC ≅ ΔDEF, when
∠BAC = ∠EFD
∠ACB = ∠EDF
∠ABC = 2∠DEF
∠ABC = ∠DEF
Q.8
If angle bisector of a triangle bisects the opposite side, then what type of triangle is it?
Right angled
Equilateral
Isosceles and equilateral
Isosceles
Q.9
In a ΔABC, AB = BC, ∠B = x° and ∠A = (2x - 20)°, Then ∠B is :
54°
30°
40°
44°
Q.10
If in a triangle ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $$\frac{{AD}}{{BD}}$$ = $$\frac{3}{5}$$. If AC = 4 cm, then AE is
1.5 cm
2.0 cm
1.8 cm
2.4 cm
Q.11
In a ΔABC, ∠A + ∠B = 118°, ∠A + ∠C = 96°. Find the value of ∠A.
36°
40°
30°
34°
Q.12
For a triangle ABC, D and E are two points on AB and AC such that AD = $$\frac{1}{4}$$ AB, AE = $$\frac{1}{4}$$ AC. If BC = 12 cm, then DE is :
5 cm
4 cm
3 cm
6 cm
Q.13
In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively. If AB = 2AD, then DE : BC is
2 : 3
2 : 1
1 : 2
1 : 3
Q.14
In a triangle ABC, ∠A = 90°, ∠C = 55°, $${AD}$$ ⊥ $${BC}$$. What is the value of ∠BAD ?
35°
60°
45°
55°
Q.15
Angle between the internal bisectors of two angles of a triangle ∠B and ∠C is 120°, then ∠A is :
20°
30°
60°
90°
Q.16
G is the centroid of the equilateral ΔABC. If AB = 10 cm then length of AG is ?
$$\frac{{5\sqrt 3 }}{3}\,cm$$
$$\frac{{10\sqrt 3 }}{3}\,cm$$
$$5\sqrt 3 \,cm$$
$$10\sqrt 3 \,cm$$
Q.17
In ΔABC, ∠A + ∠B = 65°, ∠B + ∠C = 140°, then find ∠B.
40°
25°
35°
20°
Q.18
BL and CM are medians of ΔABC right-angled at A and BC = 5 cm. If BL = $$\frac{{3\sqrt 5 }}{2}$$ cm, then the length of CM is
$$2\sqrt 5 $$ cm
$$5\sqrt 2 $$ cm
$$10\sqrt 2 $$ cm
$$4\sqrt 5 $$ cm
Q.19
The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the smallest angle is :
30°
60°
45°
90°
Q.20
ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with center O has been inscribed inside ΔABC. The radius of the circle is
1 cm
2 cm
3 cm
4 cm
Q.21
If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then
PQR must be an equilateral triangle
PQ + QR = PQR + AB
PQ + QR = PR + 2AB
PQR must be a right angled
Q.22
In a ΔABC ∠A : ∠B : ∠C = 2 : 3 : 4. A line CD drawn || to AB, then the ∠ACD is :
40°
60°
80°
20°
Q.23
ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If ∠CBE = ∠ACF = 130°, then the value of ∠GAB is :
100°
80°
130°
90°
Q.24
ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to
45°
90°
30°
60°
Q.25
If two angles of a triangle are 21° and 38°, then the triangle is :
Right-angled triangle
Acute-angled triangle
Obtuse-angled triangle
Isosceles triangle
Q.26
In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is
120°
60°
30°
90°
Q.27
In triangle ABC, ∠BAC = 75°, ∠ABC = 45°, $$\overline {BC} $$ is produced to D. If ∠ACD = x°, then $$\frac{x}{3}$$% of 60° is
30°
48°
15°
24°
Q.28
ABC is a right angled triangled, right angled at C and P is the length of the perpendicular from C on AB. If a, b and c are the length of the sides BC, CA and AB respectively, then
$$\frac{1}{{{p^2}}} = \frac{1}{{{b^2}}} - \frac{1}{{{a^2}}}$$
$$\frac{1}{{{p^2}}} = \frac{1}{{{a^2}}} + \frac{1}{{{b^2}}}$$
$$\frac{1}{{{p^2}}} + \frac{1}{{{a^2}}} = - \frac{1}{{{b^2}}}$$
$$\frac{1}{{{p^2}}} = \frac{1}{{{a^2}}} - \frac{1}{{{b^2}}}$$
Q.29
A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then
AB
2
+ CD
2
= AD
2
+ BC
2
CD
2
+ BD
2
= 2AD
2
AB
2
+ AC
2
= 2AD
2
AB
2
= AD
2
+ BC
2
Q.30
In a right-angle ΔABC, ∠ABC = 90°, AB = 5 cm and BC = 12 cm. The radius of the circumcircle of the triangle ABC is
7.5 cm
6 cm
6.5 cm
7 cm
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