True False[1 Marks ]

Question 11 Mark

The following statements are true (T) and which are false (F)?
If angles forming a linear pair are equal, then each of these angles is of measure 90°.

Answer

True
Solution:
Let one of the angle in the linear pair be x°. Then, other angle also becomes equal to x°.
Therefore, by the defination of linear pair, we get:
x + x = 180°
2x = 180°
$\text{x}=\frac{180^\circ}{2}$
x = 90°
Hence, if angles forming a linear pair are equal, then each of these angles is of measure 90°.

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Question 21 Mark

The following statements are true (T) and which are false (F)?
Angles forming a linear pair are supplementary.

Answer

True
Solution:
As the sum of the angles forming a linear pair is 180°.

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Question 31 Mark

The following statements are true (T) and which are false (F)? Give reasons.
If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Answer

False
Explanation: Theoram states: If a transversal intersects two parallel lines then the pair of alternate interior angles is equal.

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Question 41 Mark

The following statements are true (T) and which are false (F)?
Angles forming a linear pair can both be acute angles.

Answer

False
Solution:
Let us assume one of the angle in a linear pair be x;
Such that x° < 90°, that is, an acute angle.
Therefore, the other angle in the linear pair becomes (180 - x)°, which clearly cannot be acute.

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Question 51 Mark

The following statements are true (T) and which are false (F)? Give reasons.
If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

Answer

True
Explanation:
Let l and m are two parallel lines. And transversal t intersects l and m making two pair of alternate interior angles, $\angle{1},\angle{2}$ and $\angle{3},\angle{4}.$

We need to prove that $\angle{1}=\angle{2}$ and $\angle{3}=\angle{4}.$ We have, $\angle{2}=\angle{5}$ [Vertically opposite angles] Again, $\angle{3}=\angle{6}$ [Corresponding angles] Hence, $\angle{1}=\angle{2}$ and $\angle{3}=\angle{4}.$

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Question 61 Mark

The following statements are true (T) and which are false (F)?
If two adjacent angles are equal, then each angle measures 90°.

Answer

False
Solution:
As the statement is incomplete in itself.

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Question 71 Mark

The following statements are true (T) and which are false (F)? Give reasons.
Two lines parallel to the same line are parallel to each other.

Answer

True
Explanation:The figure is given as follows:

It is given that l || m and m || n We need to show that l || m We have l || m, thus, corresponding angles should be equal. That is, $\angle{1}=\angle{2}$ Similarly, $\angle{3}=\angle{2}$ Therefore, $\angle{1}=\angle{3}$ But these are the pair of corresponding angles. Therefore, l || m.

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Question 81 Mark

The following statements are true (T) and which are false (F)? Give reasons.
If two lines are intersected by a transversal, then corresponding angles are equal.

Answer

False
Explanation:
The above statement holds good if the lines are parallel only.

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Question 91 Mark

The following statements are true (T) and which are false (F)? Give reasons.
Two lines perpendicular to the same line are perpendicular to each other.

Answer

False
Explanation:The figure can be drawn as follows:

Here, $\text{l}\perp\text{n}$ and $\text{m}\perp\text{n}$ It is given that $\text{l}\perp\text{n},$ therefore, $\angle{1}=90^\circ\dots(\text{i})$ Similarly, we have $\text{m}\perp\text{n},$ therefore, $\angle{2}=90^\circ\dots(\text{ii})$ From (i) and (ii), we get: $\angle{1}=\angle{2}$ But these are the pair of corresponding angles. Theorem states: If a transversal intersects two lines in such a way that a pair of correspondung angles is equal, then the two lines are parallel. Thus, we can say that l || m.

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MATHS True False[1 Marks ]

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