Question 2
Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.
Perpendicular lines meet at a right angle, which is 90 degrees.
Step 1 — Understanding Perpendiculars on Dot Paper
On dot paper, we can draw lines connecting dots. Horizontal lines go straight across. Vertical lines go straight up and down. Diagonal lines connect dots that are not directly horizontal or vertical. To draw a perpendicular line, we need to make a perfect square corner.
Step 2 — Perpendicular to a Horizontal Line
Look at the top-left line in the diagram. This line is a horizontal line. A line perpendicular to a horizontal line must be a vertical line. Choose any dot on the given horizontal line. Draw a new line straight down or straight up from that dot to another dot. This new vertical line is perpendicular.
Step 3 — Perpendicular to a Vertical Line
Look at the middle-right line in the diagram. This line is a vertical line. A line perpendicular to a vertical line must be a horizontal line. Choose any dot on the given vertical line. Draw a new line straight left or straight right from that dot to another dot. This new horizontal line is perpendicular.
Step 4 — Perpendicular to a Diagonal Line (Up-Right)
Look at the bottom-left diagonal line. This line goes one dot up for every one dot to the right. A line perpendicular to it must go one dot down for every one dot to the right. Choose any dot on this diagonal line. From that dot, draw a new line one dot to the right and one dot down. This new diagonal line is perpendicular.
Step 5 — Perpendicular to a Diagonal Line (Up-Left)
Look at the bottom-right diagonal line. This line goes one dot down for every one dot to the right. A line perpendicular to it must go one dot up for every one dot to the right. Choose any dot on this diagonal line. From that dot, draw a new line one dot to the right and one dot up. This new diagonal line is perpendicular.
Answer
(i) For the horizontal line, draw a vertical line from one of its dots. (ii) For the vertical line, draw a horizontal line from one of its dots. (iii) For the diagonal line going up-right, draw a diagonal line going down-right from one of its dots. (iv) For the diagonal line going up-left, draw a diagonal line going up-right from one of its dots.
More questions in FIO
List all the linear pairs and vertically opposite angles you observe in Fig. 5.3:
Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.
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?
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.
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?
In Fig. 5.13, which line is parallel to line a — line b or line c? How do you decide this?
Can you draw a line parallel to , that goes through point A? How will you do it with the tools from your geometry box? Describe your method.
Find the angles marked below.
Find the angle represented by .
In the figures below, what angles do and stand for?
In Fig. 5.33, and . Find angles , ,
In Fig. 5.34, is parallel to CD and CD is parallel to EF. Also, EA is perpendicular to AB. If , find the values of and .
What is the measure of angle in Fig. 5.35?
[Hint: Draw lines parallel to LM and PQ through points N and O.]