Triangles Test

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Triangles Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

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

A
Included

B
Excluded

C
Adjacent

D
Any

Solution

Two sides and an included angle will fulfill the condition of the $$SAS$$ rule of congruence so, the two triangles will be equal. Hence,
Two triangles are congruent if the two sides and the $$\underline{\text{included}}$$ angle are equal to the two sides and the included angle of another triangle.
Question 2
1 / -0

If ____sides of a triangle are respectively equal to the ____ sides of the other triangle, then the triangles are congruent.

A
Three

B
Two

C
One

D
None

Solution

If all the three sides of the triangle are equal to corresponding three sides of other triangle. Both the triangles will be congruent by SSS rule.
Question 3
1 / -0

In a right triangle, the hypotenuse is the $$.......$$ side

A
Largest

B
Shortest

C
Can be largest or shortest

D
None of these

Solution

In a right triangle, using Pythagoras theorem,
$$Hypotenuse^2 = perpendicular^2 + base^2$$
Thus, Hypotenuse is the largest side.
Question 4
1 / -0

In $$\Delta ABC$$, AB = AC and AD is perpendicular to BC. State the property by which $$\Delta ADB\, \cong\, \Delta ADC$$.

A
SAS property

B
SSS property

C
RHS property

D
ASA property

Solution

In $$\triangle ADB$$ and $$\triangle ADC$$
$$AB=AC$$ (given)
$$AD=AD$$ (common side)
$$\angle ADB=\angle ADC=90^{\circ}$$ (As$$AD\perp BC)$$
$$\therefore \triangle ADB\cong \triangle ADC$$ by $$RHS$$ property.
Question 5
1 / -0

In $$\triangle PQR$$, $$\angle P={ 50 }^{ 0 }$$ and $$\angle R={ 70 }^{ 0 }$$. Name
i) the shortest side.
ii)the longest side of the triangle

A
i)$$PQ$$,

(ii)$$QR$$

B
i)$$PR$$,

(ii)$$PQ$$

C
i)$$QR$$,

(ii)$$PQ$$

D
i)$$PQ$$,

(ii)$$PR$$

Solution

In $$\triangle PQR$$, $$\angle P = 50^{\circ}$$, $$\angle R = 70^{\circ}$$
Sum of angles of the triangle = 180
$$\angle P + \angle Q + \angle R = 180$$
$$50 + \angle Q + 70 = 180$$
$$\angle Q = 60^{\circ}$$
Side opposite smaller angle is shorter and side opposite to larger angle is larger.
Hence, $$QR$$ is the smallest side, $$PQ$$ is the largest side.
Question 6
1 / -0

In a $$\Delta\, ABC$$, if $$\angle B$$ is an obtuse angle, then the longest side is:

A
$$AB$$

B
$$BC$$

C
$$AC$$

D
none

Solution

Side opposite to the largest angle is the longest side.
It is given that, $$\angle B$$ is obtuse , so the other two angles must be acute angles.
So, $$\angle B$$ is the largest angle and the side opposite to it is $$AC$$

Hence, $$AC$$ is the longest side.
Question 7
1 / -0

In the following fig. if $$AB=AC$$ and $$BD= DC$$ then $${\angle ADC}$$ =

A
$${60^ 0}$$

B
$${120^ 0}$$

C
$${90^ 0}$$

D
None

Solution

In $$\triangle ABD$$ and $$\triangle ACD$$
$$AB=AC$$ (Given)
$$BD=DC$$ (Given)
$$AD=AD$$ (Common side)
$$\therefore \triangle ABD\cong ACD$$ by $$SSS$$ criteria.
Now corresponding angles of congruent triangles are equal
$$\Rightarrow \angle ADB=\angle ADC$$
Now $$\angle ADB+\angle ADC=180^{\circ}$$ (Adjacent angles on staraight line)
$$\Rightarrow \angle ADC+\angle ADC={ 180 }^{ \circ }\\ \Rightarrow 2\angle ADC={ 180 }^{ \circ }\\ \Rightarrow \angle ADC={ 90 }^{ \circ }\\ $$
Question 8
1 / -0

The sum of lengths of any two sides of a triangle is always_________the third side.

A
greater than

B
less than

C
equal to

D
none of these

Solution

The sum of lengths of any two sides of a triangle is always greater than the third side.
For e.g.. in $$\triangle ABC$$, we have
$$AC+BC>AB$$.
Question 9
1 / -0

If the angles of a triangle are $$30^{\circ},60^{\circ},90^{\circ}$$, then what is the ratio of corresponding sides?

A
$$\;1\,\colon\,2\,\colon\,3$$

B
$$\;1\,\colon\,1\,\colon\,\sqrt{2}$$

C
$$\;1\,\colon\,\sqrt{3}\,\colon\,3$$

D
$$\;1\,\colon\,\sqrt{2}\,\colon\,2$$

Solution

Since the side opposite to the greatest angle is the greatest and the ratio of sides $$=$$ Ratio of corresponding angles
Thus, the ratio of corresponding sides $$=30\,\colon\,60\,\colon\,90=1\,\colon\,2\,\colon\,3$$.
Question 10
1 / -0

In the $$\triangle ABC$$,we have $$\angle A>\angle B>\angle C$$, then determine the shortest and the longest side of the triangle.

A
Shortest side is $$AB$$ and the longest side is $$BC$$

B
Shortest side is $$BC$$ and the longest side is $$AB$$

C
Shortest side is $$AB$$ and the longest side is $$AC$$

D
Shortest side is $$AC$$ and the longest side is $$BC$$

Solution

Given, $$\angle A > \angle B > \angle C$$

Hence, $$BC > AC > AB$$ (Side opposite largest angle is the longest and vice versa)

Thus, $$BC$$ is the largest and $$AB$$ is the shortest.

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Triangles Test - 23

Result

Triangles Test - 23

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SHARING IS CARING

Question 1

Included

Excluded

Adjacent

Any

Solution

Question 2

Three

Two

One

None

Solution

Question 3

Largest

Shortest

Can be largest or shortest

None of these

Solution

Question 4

SAS property

SSS property

RHS property

ASA property

Solution

Question 5

i)$$PQ$$, (ii)$$QR$$

i)$$PR$$, (ii)$$PQ$$

i)$$QR$$, (ii)$$PQ$$

i)$$PQ$$, (ii)$$PR$$

Solution

Question 6

$$AB$$

$$BC$$

$$AC$$

none

Solution

Question 7

$${60^ 0}$$

$${120^ 0}$$

$${90^ 0}$$

None

Solution

Question 8

greater than

less than

equal to

none of these

Solution

Question 9

$$\;1\,\colon\,2\,\colon\,3$$

$$\;1\,\colon\,1\,\colon\,\sqrt{2}$$

$$\;1\,\colon\,\sqrt{3}\,\colon\,3$$

$$\;1\,\colon\,\sqrt{2}\,\colon\,2$$

Solution

Question 10

Shortest side is $$AB$$ and the longest side is $$BC$$

Shortest side is $$BC$$ and the longest side is $$AB$$

Shortest side is $$AB$$ and the longest side is $$AC$$

Shortest side is $$AC$$ and the longest side is $$BC$$

Solution

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i)$$PQ$$,

(ii)$$QR$$

i)$$PR$$,

(ii)$$PQ$$

i)$$QR$$,

(ii)$$PQ$$

i)$$PQ$$,

(ii)$$PR$$