Triangles Test

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Triangles Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

An exterior angle of the triangle is 110^o , One of the opposite interior angle is 50^o . What are the other two angles ?

A
55^o, 55^o

B
70^o, 50^o

C
50^o , 80^o

D
60^o and 70^o

Solution

Explanation:

Let the other opposite interior angle be x and the remaining angle of the triangle be z.

Sum of the opposite two interior angle = Exterior angle
50^o+ x = 110^o

=> x = 60^o
Now , 60^o+ 50^o + z =180^o (Angle sum property)
=> z = 70^o

Therefore, the other two angles of the triangle = 60^o and 70^o
Question 2
1 / -0

Which of the following statements is true?

A
A triangle can have two obtuse angles

B
A triangle can have two right angles

C
All are true

D
A triangle can have two acute angles

Solution

Explanation:

A triangle can have two or even all three acute angles(in case of an equilateral triange) but it cannot have two right angles or two obtuse angles as the sum of the interior angles of a triangle is 180^o and two right angles or two obtuse angles wouls sum up to 180^o or more leaving the no space for the third angle.
Question 3
1 / -0

If all the altitudes from the vertices to the opposite sides of a triangle are equal, then the triangle is

A
Isosceles

B
Equilateral

C
Scalene

D
Right-angled

Solution

Explanation:

In an equilateral triangle all the altitudes,sides, angles, perpendicular bisectors, medians and angular bisectors are equal.
Question 4
1 / -0

If O is any point in the interior of △ABC , then, which of the following is true?

A
(OA+OB+OC)< 1/2 (AB+BC+CA)

B
None

C
(OA+OB+OC) > 1/2 (AB+BC+CA)

D
(OA+OB+OC) > (AB+BC+CA)

Solution

Explanation:

Sum of any two sides of a triangle is greater than the third side.

Join O with all sides of the triangle, we have

OA+OB > AB .........(i)

OA+OC > AC..........(ii)

and, OB+OC > BC .....(iii)

Adding the three inequalities i.e. (i) + (ii) + (iii), we get

2(OA+OB+OC) > AB+BC+AC

i.e.(OA+OB+OC) > 1/2 (AB+BC+CA).
Question 5
1 / -0

Which of the following is not a criterion for congruence of triangles?

A
ASA

B
SSS

C
SAS

D
SSA

Solution

Explanation:

The criteria for congruence of triangles are SSS(Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side- Angle) and RHS (Right angle- Hypotenuse-Side)
Question 6
1 / -0

The perimeter of a triangle is 36 cm and its sides are in the ratio a:b:c = 3:4:5 then a,b,c are respectively:

A
15cm, 12cm, 9 cm

B
9 cm, 15 cm, 12cm

C
12cm, 9cm, 15cm

D
9cm, 12cm, 15cm

Solution

Explanation:

Let the three sides a, b , c be 3x, 4x and 5x respectively

Then according to the conditions given in the question, we have

3x + 4x + 5x = 36

12x = 36

x = 3 cm

Thus, the three sides are :

a = 3 x 3 = 9 cm,

b = 4 x 3 =12 cm and

c = 5 x 3 = 15 cm
Question 7
1 / -0

It is given that △ABC ≅ △FDE in which AB = 5 cm, ∠B = 40^∘,∠A = 80^∘and FD = 5 cm. Then,which of the following is not true?

A
∠E = 60^∘

B
∠C =60^∘

C
∠D =60^∘

D
∠F=80^∘

Solution

Explanation:

Since, △ABC≅△FDE,

Therefore, ∠B = ∠D = 40^o, ∠A = ∠F = 80^o and ∠C = ∠E = 60^o
Question 8
1 / -0

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 cm

C
3.8 cm

D
3.4 cm

Solution

Explanation:

Given that: Two sides of triangle are 5 cm and 1.5 cm. We know that the sum of two sides of the triangle is always greater than the third side. Hence, 3.4 cm cannot be the third side. If it is the third side the sum of 3.4 cm and 1.5 cm will be smaller than 5 cm, so, the triangle will not be possible.
Question 9
1 / -0

In △ABC and △DEF, AB = DE and ∠A = ∠D.Then , the two triangles will be congruent by SAS axiom if:

A
AC = DF.

B
AC = DE

C
BC = EF

D
BC = DE

Solution

Explanation:

The SAS rule states that :

If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

Here, in ΔABC, the two sides are AB and AC and the included angle is ∠A. For ΔDEF, the two corresponding sides are DE and DF and the included angle is ∠D

Hence,the two triangles will be congruent by SAS axiom if AC = DF.
Question 10
1 / -0

In △ABC, ∠A = 35∘ and ∠B = 65∘, then the longest side of the triangle is:

A
AB

B
None of these

C
AC

D
BC

Solution

Explanation:

As per angle sum property, ∠A +∠B+∠C=180^∘

Hence, 35^o + 65^o + ∠C =180^o

=> ∠C = 80^o which is the greatest angle.

We know that the side opposite to the greatest angle i.e AB would be the greatest.

Hence, AB is the longest side.

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Re-Attempt Weekly Quiz Competition

Triangles Test - 1

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Triangles Test - 1

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SHARING IS CARING

Question 1

55o, 55o

70o, 50o

50o , 80o

60o and 70o

Solution

Question 2

A triangle can have two obtuse angles

A triangle can have two right angles

All are true

A triangle can have two acute angles

Solution

Question 3

Isosceles

Equilateral

Scalene

Right-angled

Solution

Question 4

(OA+OB+OC)< 1/2 (AB+BC+CA)

None

(OA+OB+OC) > 1/2 (AB+BC+CA)

(OA+OB+OC) > (AB+BC+CA)

Solution

Question 5

ASA

SSS

SAS

SSA

Solution

Question 6

15cm, 12cm, 9 cm

9 cm, 15 cm, 12cm

12cm, 9cm, 15cm

9cm, 12cm, 15cm

Solution

Question 7

∠E = 60∘

∠C =60∘

∠D =60∘

∠F=80∘

Solution

Question 8

3.6 cm

4 cm

3.8 cm

3.4 cm

Solution

Question 9

AC = DF.

AC = DE

BC = EF

BC = DE

Solution

Question 10

AB

None of these

AC

BC

Solution

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55^o, 55^o

70^o, 50^o

50^o , 80^o

60^o and 70^o

∠E = 60^∘

∠C =60^∘

∠D =60^∘

∠F=80^∘