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Maths True False With Reason

Triangle And lts Angles · Maharashtra Board STD 9 (MSBSHSE - English Medium). 11 questions.

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True False With Reason

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11 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
The following statements are true (T) and which are false (F):
An exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Answer
True. Explanation: According to exterior angle theorem,$\text{ext.x}=\angle\text{CAB}+\angle\text{CBA}$
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Question 22 Marks
The following statements are true (T) and which are false (F):
An exterior angle of a triangle is greater than the opposite interior angles.
Answer
True. Explanation: According to exterior angle theorem,$\text{ext.x}=\angle\text{CAB}+\angle\text{CBA}$
Since, the exterior angle is the sum of its interior angels. Thus,$\text{ext.x}>\angle\text{CAB}$
$\text{ext.x}>\angle\text{CBA}$
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Question 32 Marks
The following statements are true (T) and which are false (F):
Sum of the three angles of a triangle is 180°.
Answer
True. Explanation: According to the angle sum property of the triangle In $\triangle\text{ABC}$$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
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Question 42 Marks
The following statements are true (T) and which are false (F):
All the angles of a triangle can be equal to 60°.
Answer
True.Explanation:

According to the angle sum property of the triangle In $​​\triangle\text{ABC}$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ Now, if all the three angles of a triangle are equal to 60º Then,$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
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Question 52 Marks
The following statements are true (T) and which are false (F):
A triangle can have two obtuse angles.
Answer
False.Explanation:

According to the angle sum property of the triangle In$\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ Now, if a triangle of a triangle are equal to 60º Then,$\angle\text{A}+\angle\text{B}+\angle\text{C}>180^\circ$
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Question 62 Marks
The following statements are true (T) and which are false (F):
A triangle can have two right angles.
Answer
False. Explanation: According to the angle sum property of the triangle In $\triangle\text{ABC}$$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if there are two right angles in the triangle Let $\angle\text{B}=\angle\text{C}=90^\circ$ Then,$\angle\text{A}+90^\circ+90^\circ=180^\circ$
$\angle\text{A}+180^\circ=180^\circ$
$\angle\text{A}=180^\circ-180^\circ$
$\angle\text{A}=0^\circ$
(This is not possible.)
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Question 72 Marks
The following statements are true (T) and which are false (F):
All the angles of a triangle can be less than 60°.
Answer
False. Explanation: According to the angle sum property of the triangle In $\triangle\text{ABC}$$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, If all the three angles of a triangle is less than 60º Then,$\angle\text{A}+\angle\text{B}+\angle\text{C}<180^\circ$
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Question 82 Marks
The following statements are true (T) and which are false (F):
If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
Answer
True. Explanation: According to the angle sum property of the triangle In $\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ Now, if a right angled triangle Then,$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$90^\circ+\angle\text{B}+\angle\text{C}=180^\circ$
$\angle\text{B}+\angle\text{C}=90^\circ$
Also if one of the angle's is obtuse$\angle\text{B}+\angle\text{C}>90^\circ$
This is not possible. Thus, if one angle of a triangle is obtuse, then it cannot be a right angled triangle.
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Question 92 Marks
The following statements are true (T) and which are false (F):
An exterior angle of a triangle is less than either of its interior opposite angles.
Answer
False. Explanation: According to the exterior angle property, an exterior angle of a equal to the sum of the two opposite interior angles. In $\triangle\text{ABC}$ Let x be the exterior angle So,$\text{x}=\angle\text{CAB}+\angle\text{CBA}$
Now, if x is less than either of its interior opposite angles$\text{x}<\angle\text{CAB}+\angle\text{CBA}$
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Question 102 Marks
Which of the following statements are true (T) and which are false (F):
A triangle can have at most one obtuse angles.
Answer
True.Explanation:

According to the angle sum property of the triangle In $\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ Now, if a triangle will have more than one obtuse angle Then,$\angle\text{A}+\angle\text{B}+\angle\text{C}>180^\circ$
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Question 112 Marks
The following statements are true (T) and which are false (F):
All the angles of a triangle can be greater than 60°.
Answer
False. Explanation: According to the angle sum property of the triangle In $\triangle\text{ABC}$$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if all the three angles of a triangle is greater than 60º Then,$\angle\text{A}+\angle\text{B}+\angle\text{C}>180^\circ$
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