True False With Reason

Question 12 Marks

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 22 Marks

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 32 Marks

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

FalseExplanation:
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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Question 42 Marks

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

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

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Question 52 Marks

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

TrueExplanation:
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 62 Marks

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 72 Marks

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

TrueExplanation:
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 82 Marks

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 92 Marks

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

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

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