**1. Which of the following are models for perpendicular lines:**

**(a) The adjacent edges of a table top**

**Ans. **Figure showing adjacent edges which are perpendicular to each other. Therefore, yes, the adjacent edges of a table top is model of a perpendicular line

**(b) The lines of a railway track.**

**Ans. **Figure showing the lines of a railway track which are parallel to each other. Therefore, No the lines of a railway track are not model of a perpendicular line

**(c) The line segments forming the letter ‘L’. **

Figure showing the line segments forming the letter ‘L’ which are perpendicular to each other.

Therefore, yes, the line segments forming the letter ‘L’ is model of a perpendicular line

**(d) The letter V**

**Ans. **Figure showing the letter V which are not perpendicular to each other. They form an acute angle. Therefore, no, the letter V is not a model of a perpendicular line

**2. Let PQ be the perpendicular to the line segment XY. Let PQ and XY intersect in the point A. What is the measure of ∠PAY?**

**Sol. **It is given that PQ is perpendicular to the line segment XY. IT means wherever they intersect, they form a right angle (90^{o}) at the intersecting point.

Here, they intersect at point A.

Hence, **∠**PAY = 90^{o} **Ans.**

**(3) There are two set-squares in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?**

**Ans**. There are two set squares in the box.

The measure of angles in one set square are 30^{0}, 60^{0} and 90^{0}

The measure of angles in other set square are 45^{0}, 45^{0} and 90^{0} Yes, the angle measure 90^{0} is common in both set squares

**(4)** **Study the diagram. The line l is perpendicular to line m**

**(a)** **Is CE = EG?****Sol**. Here, CE = 2 units and EG = 2 units

Therefore, CE = EG = 2 units

Yes, CE = EG ** Ans.**

**(b)** **Does PE bisect CG?****Sol. **Here, CE = 2 units and EG = 2 units

Therefore, CE = EG = 2 units

Hence, Yes, PE bisect CG** Ans.**

**(c) Identify any two-line segments for which PE is the perpendicular bisector.****Sol. **Perpendicular bisector means forming 90o and also dividing the line segment into two equal parts.

It is given that they are perpendicular to each other

Here, DE = EF = 1 units

And also, BE = EH = 3 units

Therefore, the two line segments for which PE is the perpendicular bisector are DF and BH.** Ans.**

**(d) Are these true?****(i) AC > FG****Ans. **True

Reason – From the figure, AC = 2 units and FG = 1 unit

Therefore, yes, AC > FG

**(ii) CD = GH****Ans. **True

Reason – CD = 1 unit and GH = 1 unit

Therefore, yes, CD = GH

**(iii) BC < EH.****Ans. **True

Reason – BC = 1 unit and EH = 3 unit Therefore, yes, BC < EH