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Understanding Elementary Shapes
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.
Solution: (a) Yes, the adjacent edges of a table top are perpendicular to each other.
(b) No, the lines of a railway track are parallel to each other.
(c) Yes, the line segments forming the letter 'L' are perpendicular to each other.
(d) No, the line segments of letter 'V' are making an acute angle.
2. Let be the perpendicular to the line segment . Let and intersect in the point A. What is the measure of ∠PAY ?
Solution: The figure looks like shown below:
The measure of ∠PAY = 900.
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?
Solution: The measure of angles in two set squares in the box are:
30°, 60°, 90º and the other set square has 45°, 45° and 90°
Yes, the angle of measure 90° is the common angle between the two set-squares.
4. Study the diagram. The line l is perpendicular to line m
(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
(iii) BC < EH
Solution: (a) CE = 5 - 3 = 2 units.
EG = 7 - 5 = 2 units.
Yes, CE = EG.
(b) As, CE = EG, hence PE bisects CG.
(c) From the figure, PE is the perpendicular bisector for the line segment DF and CG.
(d) (i) True, AC = 2 units and FG = 1 unit
Hence, AC > FG
(ii) True, CD = 1 unit and GH = 1 unit.
Hence, CD = GH
(iii) True, BC = 1 unit and EH = 3 units.
Hence, BC < EH
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