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Arithmetic Ability
Triangles
Quiz 5
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Q.1
Consider the following statements : I. Every equilateral triangle is necessarily an isosceles triangle. II. Every right-angled triangle is necessarily an isosceles triangle. III. A triangle in which one of the median is perpendicular to the side it meets, is necessarily an isosceles triangle. The correct statements are:
I and II
II and III
I and III
I, II and III
Q.2
Consider the following statements : I. Three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent. II. If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent. Of these statements :
I and II both are true
I is true and II is false
I is false and II is true
None of these
Q.3
In ΔABC, AD ⊥ BC, then
AB
2
- BD
2
= AC
2
- CD
2
AB
2
+ BD
2
= AC
2
- CD
2
AB
2
- BD
2
= AC
2
+ CD
2
AB
2
- AC
2
= BD
2
+ CD
2
Q.4
ΔABC be a right-angled triangle where ∠A = 90° and AD ⊥ BC. If ar (ΔABC) = 40 cm
2
, ar (ΔACD) = 10 cm
2
and AC = 9 cm, then the length of BC is
12 cm
18 cm
4 cm
6 cm
Q.5
A triangle cannot be drawn with the following three sides
2m, 3m, 4m
3m, 4m, 8m
4m, 6m, 9m
5m, 7m, 10m
Q.6
Which of the following is a true statement
Two similar triangles are always congruent
Two similar triangles have equal areas
Two triangles are similar if their corresponding sides are proportional
Two polygons are similar if their corresponding sides are proportional
Q.7
The point of intersection of the altitudes of a triangle is called its:
Incentre
Excentre
Orthocentre
Centroid
Q.8
In ΔPQR, PS is the bisector of ∠P and PT ⊥ OR, then ∠TPS is equal to:
∠Q + ∠R
90° + $$\frac{1}{2}$$ ∠Q
90° - $$\frac{1}{2}$$ ∠R
$$\frac{1}{2}$$ (∠Q - ∠R)
Q.9
In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is:
3 cm
4 cm
6 cm
12 cm
Q.10
Two right angled triangles are congruent if :
I. The hypotenuse of one triangle is equal to the hypotenuse of the other.
II. A side for one triangle is equal to the corresponding side of the other.
III. Sides of the triangles are equal.
IV. An angle of the triangle are equal.
Of these statements, the correct ones are combination of:
I and II
II and III
I and III
IV only
Q.11
In case of an acute angled triangle, its orthocenter lies:
Inside the triangle
Outside the triangle
On the triangle
On one of the vertex of the triangle
Q.12
If the measure of the angles of a triangle are in the ratio 1 : 2 : 3 and if the length of the smallest side of the triangle is 10 cm, then the length of the longest side is:
20 cm
25 cm
30 cm
35 cm
Q.13
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :
6 cm
8 cm
7 cm
10 cm
Q.14
In a ΔABC, ∠A + ∠B = 75° and ∠B + ∠C = 140°, then ∠B is:
40°
35°
50°
45°
Q.15
In an equilateral triangle ABC, G is the centroid. Each side of the triangle is 6 cm. The length of AG is:
$$2\sqrt 2 $$ cm
$$3\sqrt 2 $$ cm
$$2\sqrt 3 $$ cm
$$3\sqrt 3 $$ cm
Q.16
The in-radius of an equilateral triangle is of length 3 cm. Then the length of each of its medians is
12 cm
$$\frac{9}{2}$$ cm
4 cm
9 cm
Q.17
In ΔABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is
2 : 1
1 : 2
4 : 5
3 : 5
Q.18
If the circumradius of an equilateral triangle be 10 cm, then the measure of its in-radius is
5 cm
10 cm
20 cm
15 cm
Q.19
In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and ∠A = 60°, then length of AD is :
$$2\sqrt 3 $$
$$\frac{{12\sqrt 3 }}{7}$$
$$\frac{{15\sqrt 3 }}{8}$$
$$\frac{{6\sqrt 3 }}{7}$$
None of these
Q.20
I is the incentre of ΔABC, ∠ABC = 60° and ∠ACB = 50°, Then ∠BIC is
55°
125°
70°
65°
Q.21
In the adjoining figure AB, EF and CD are parallel lines. Given that GE = 5 cm, GC = 10 cm and DC = 18 cm, then EF is equal to:
11 cm
5 cm
6 cm
9 cm
Q.22
ΔABC is similar to ΔDEF is area of ΔABC is 9 sq. cm. and area of ΔDEF is 16 sq. cm. and BC = 21 cm. Then the length of EF will be:
5.6 cm
2.8 cm
3.7 cm
1.4 cm
Q.23
ABC is a triangle, PQ is line segment intersecting AB is P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and length of PQ is 18 cm. The length of BC is:
28 cm
48 cm
84 cm
42 cm
Q.24
In the following figure which of the following statements is true?
AB = BD
AC = CD
BC + CD
AD < Cd
Q.25
AB and CD bisect each other at O. If AD = 6 cm. Then BC is :
5.9 cm
4.8 cm
6 cm
7 cm
Q.26
In a triangle ABC,∠ A = 90°, AL is drawn perpendicular to BC, Then ∠BAL is equal to:
∠ALC
∠ACB
∠BAC
∠B - ∠BAL
Q.27
In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incenter of ΔABC, ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are:
15°, 130°
15°, 125°
35°, 40°
30°, 150°
Q.28
If ΔPQR and ΔLMN are similar and 3PQ = LM and MN = 9 cm, then QR is equal to:
12 cm
6 cm
9 cm
3 cm
Q.29
In ΔABC, AC = BC and ∠ABC = 50°, the side BC is produced to D so that BC = CD then the value of ∠BAD is:
80°
40°
90°
50°
Q.30
ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?
PB = PC
PB > PC
PB < PC
PB = $$\frac{1}{2}$$ PC
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