**Understanding Elementary Shapes**

**Exercise 5.5**

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

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

(b). The lines of a railway track.

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

(d). The letter V.

Answers:

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

Perpendicular lines.

(b). The lines of a railway track.

Not perpendicular lines.

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

Perpendicular lines.

(d). The letter V.

Not perpendicular lines.

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?

m∠PAY = 90^{0}.

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?

One of the set squares is of the measure 30^{0}-60^{0}-90^{0} and the measure of the other 45^{0}-45^{0}-90^{0}. The measure of the corner with 90° is common to both the set-squares.

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

(a). Is CE = EG?

Yes.

CE = 2 cm and EG = 2 cm

Therefore, CE = EG.

(b). Does PE bisect CG?

Yes.

(c). Identify any two line segments for which PE is the perpendicular bisector.

Seg DF and Seg CG.

(d). Are these true?

(i). AC>FG

True.

(ii) CD= GH

True.

(iii). BC < EH.

True.

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