Parallel and Intersecting Lines | FIO

Question 2

Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.

Question diagram 1
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Solution
Understand the Question
  • Perpendicular lines meet at a right angle (90∘90^\circ).
  • On square dot paper:
    • A horizontal line is perpendicular to a vertical line.
    • A diagonal line slanting upwards (slope +1+1) is perpendicular to a diagonal line slanting downwards (slope −1-1).

Step 1 · Perpendicular to Horizontal and Vertical Lines

Diagram 1

  • Horizontal line: A line perpendicular to a horizontal line is a vertical line. Choose any dot on the given horizontal line and draw a straight vertical line through it.
  • Vertical line: A line perpendicular to a vertical line is a horizontal line. Choose any dot on the given vertical line and draw a straight horizontal line through it.

Step 2 · Perpendicular to Diagonal Lines

  • Diagonal line (up-right): The line rises 11 dot up for every 11 dot to the right. A perpendicular line goes 11 dot down for every 11 dot to the right (down-right diagonal).
  • Diagonal line (down-right): The line goes 11 dot down for every 11 dot to the right. A perpendicular line goes 11 dot up for every 11 dot to the right (up-right diagonal).
Answer
  • Draw a vertical line perpendicular to the horizontal line.
  • Draw a horizontal line perpendicular to the vertical line.
  • Draw a down-right diagonal line perpendicular to the up-right diagonal line.
  • Draw an up-right diagonal line perpendicular to the down-right diagonal line.
Common Mistakes
  • Grid Angle Confusion: Connecting random diagonal dots without ensuring the angle formed is exactly 90∘90^\circ. On a square grid, a diagonal line moving 11 unit right and 11 unit up is only perpendicular to one moving 11 unit right and 11 unit down.
  • Non-alignment on Dots: Drawing lines that do not pass precisely through the grid dots, leading to inaccurate angles.

More questions in FIO

Q1

List all the linear pairs and vertically opposite angles you observe in Fig. 5.3:

Q2

Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.

Q3

In Fig. 5.11, mark the parallel lines using the notation given above (single arrow, double arrow etc.). Mark the angle between perpendicular lines with a square symbol.

(a) How did you spot the perpendicular lines?

(b) How did you spot the parallel lines?

Q4

In the dot paper following, draw different sets of parallel lines. The line segments can be of different lengths but should have dots as endpoints.

Q5

Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper.

(a) Did you find it challenging to draw some of them? (b) Which ones? (c) How did you do it?

Q6

In Fig. 5.13, which line is parallel to line aa — line bb or line cc? How do you decide this?

Q7

Can you draw a line parallel to ll, that goes through point AA? How will you do it with the tools from your geometry box? Describe your method.

Q8

Find the angles marked below.

Q9

Find the angle represented by aa.

Q10

In the figures below, what angles do xx and yy stand for?

Q11

In Fig. 5.33, ∠ABC=45∘\angle ABC = 45^\circ and ∠IKJ=78∘\angle IKJ = 78^\circ. Find angles ∠GEH\angle GEH, ∠HEF\angle HEF, ∠FED\angle FED

Q12

In Fig. 5.34, ABAB is parallel to CDCD and CDCD is parallel to EFEF. Also, EAEA is perpendicular to ABAB. If ∠BEF=55∘\angle BEF = 55^\circ, find the values of xx and yy.

Q13

What is the measure of angle ∠NOP\angle \text{NOP} in Fig. 5.35?

[Hint: Draw lines parallel to LM and PQ through points N and O.]

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