EXERCISE 5.5

1) Which of the following are models for perpendicular lines:
(a) The adjacent edges of a table top.
Ans : Yes
(b) The lines of a railway track
Ans : No
(c) The line segments forming the letter ‘L’
Ans : Yes.
(d) The letter V
Ans : No.

2) Let the perpendicular to the line segment( XY)  Let ___and (XY) intersect in the line point A.What is the measure of ∠PAY ?

Ans : ∠PAY = 90˚.

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 :
                                                 

One is 30˚- 60˚- 90˚ set square., the other is a 45˚- 45˚- 90˚ set square.
The angle of measure 90˚ is common between them.

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

(a) Is CE = EG

Ans : Yes, CE and EG are equal.
(b) Does PE bisect CG?

Ans : Yes.
(c) Identify any two line segments for which PE is perpendicular bisector.

Ans : BH , DF or CG  AH.
(d) Are these true?

(1) AC > FG                (2) CD = GH        (3) BC < EH
Ans : (1) True .   (2)True     (3)   True

Do This:
Try to do rough sketches of
(a)  Scalene Acute angled triangle.
Ans :

(b)  Obtuse  angled triangle.
Ans :

(c)  Right  angled Isosceles triangle.
Ans :

(d)  Scalene  Right – angled triangle.
Ans :

Do you think it is possible to sketch
(a) an Obtuse angled equilateral triangle?
Ans : In an equilateral triangle has each angle of 60°. But an obtuse angle has to be more than 90°
∴ Not possible.

(b) a  Right – angled equilateral triangle?
Ans : If one angle is a right a angle then the sum of remaining two angles will be equal to 90º.
∴ Not possible.

(c) a triangle with two Right angles ?
Ans : If a triangle has two right angles then the third angle will be 0º.
∴ Not possible.