Congruence of Triangles Test

Result

Congruence of Triangles Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

A
An isosceles triangle

B
An obtuse triangle

C
An equilateral triangle

D
A right-angled triangle

Solution

Let the angles of the triangle be a, b and c.

According to question,

a = b + c

Now, sum of angles of a triangle = 180°

a + b + c = 180°

a + a = 180°

a = 90°

Therefore, one angle of the triangle will be right angle.

Hence, D is the correct answer.
Question 2
1 / -0

If two sides of a triangle are 4 cm and 8 cm, then which of the following best describe the length of the third side.

A
4 < Third side < 8

B
2 < Third side < 4

C
4 < Third side < 12

D
8 < Third side < 12

Solution

Let the third side be c.

We know that the sum of two sides of a triangle is always greater than the third side,

Therefore,

4 + c > 8

c > 4

Also,

4 + 8 > c

c < 12

Therefore,

4 < Third side < 12

Hence, C is the correct answer.
Question 3
1 / -0

If the largest of an isosceles right-angled triangle is 4 cm. then, the length of the equal sides is

A
2√2 cm

B
4 cm

C
4√2 cm

D
8 cm

Solution

Let the equal sides be x.

Now, we know according to the Pythagoras theorem, the sum of the square of sides equal to the square of largest side.

Therefore,

x² + x² = (4)²

2x² = 16

x² = 8

x = 2√2 cm

Hence, A is the correct answer.
Question 4
1 / -0

If three sides of a right-angled triangle are x, y and z such that z is the largest side, then which of the following is correct?

A
x² + y² + z² = 0

B
x² + y² – z² = 0

C
x² – y² + z² = 0

D
x² – y² – z² = 0

Solution

In a right-angled triangle,

The sum of the square of two sides of a right-angled triangle equals the square of the largest side.

Therefore,

x² + y² = z²

x² + y² – z² = 0

Hence, B is the correct answer.
Question 5
1 / -0

If a, b and c are sides of a triangle, then which of the following is incorrect?

A
a + b = c

B
a + b > c

C
a + c > b

D
b + c > a

Solution

In a triangle, the sum of two sides is always greater than the third side.

Therefore,

a + b > c

a + c > b

b + c > a

Hence, A is the correct answer.
Question 6
1 / -0

If two sides of a triangle are 6 and 8 and the third side is ‘x’, then which of the following is correct?

A
6 < x < 14

B
-2 < x < 14

C
2 < x < 14

D
8 < x < 14

Solution

In a triangle, the sum of two sides is always greater than the third side.

Therefore,

x + 6 > 8

x > 2

Also,

8 + 6 > x

x < 14

So,

2 < x < 14

Hence, C is the correct answer.
Question 7
1 / -0

If a, 12, and 13 are the three sides of a right-angled triangle such that 13 is the hypotenuse, then find the value of a.

A
3

B
4

C
5

D
6

Solution

According to Pythagoras theorem, the sum of the square of two sides of a triangle equal to the square of hypotenuse.

Therefore,

a² + 12² = 13²

a² + 144 = 169

a² = 169 – 144

a² = 25

a = 5

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Re-Attempt Weekly Quiz Competition

Congruence of Triangles Test - 2

Result

Congruence of Triangles Test - 2

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Question 1

An isosceles triangle

An obtuse triangle

An equilateral triangle

A right-angled triangle

Solution

Question 2

4 < Third side < 8

2 < Third side < 4

4 < Third side < 12

8 < Third side < 12

Solution

Question 3

2√2 cm

4 cm

4√2 cm

8 cm

Solution

Question 4

x2 + y2 + z2 = 0

x2 + y2 – z2 = 0

x2 – y2 + z2 = 0

x2 – y2 – z2 = 0

Solution

Question 5

a + b = c

a + b > c

a + c > b

b + c > a

Solution

Question 6

6 < x < 14

-2 < x < 14

2 < x < 14

8 < x < 14

Solution

Question 7

3

4

5

6

Solution

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x² + y² + z² = 0

x² + y² – z² = 0

x² – y² + z² = 0

x² – y² – z² = 0