Question 4
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.
Parallel lines always stay the same distance apart and never cross each other.
Step 1 — Understanding Parallel Lines
Parallel lines are lines that always stay the same distance apart. They never meet, no matter how long they are. Think of the opposite sides of a ruler. Or the tracks of a train.
Step 2 — Finding Slope on Dot Paper
On dot paper, we can describe a line's steepness. This steepness is called its slope. We find slope by counting "rise" and "run". "Rise" is how many dots up or down. "Run" is how many dots right or left. For example, if a line goes 1 dot up and 2 dots right, its slope is 1/2. If it goes 2 dots down and 1 dot right, its slope is -2/1 or -2. Parallel lines always have the same slope.
Step 3 — Drawing Sets of Parallel Lines
We will now draw different sets of parallel lines. Each set will have lines with the same slope.
Set 1: Horizontal Parallel Lines
Horizontal lines go straight across. Their rise is always 0. Their run can be any number. Let us draw a line from dot (1, 6) to dot (5, 6). This line is horizontal. Now, let us draw another line from dot (1, 4) to dot (5, 4). This line is also horizontal. These two lines are parallel.
Set 2: Vertical Parallel Lines
Vertical lines go straight up and down. Their run is always 0. Their rise can be any number. Let us draw a line from dot (2, 8) to dot (2, 5). This line is vertical. Now, let us draw another line from dot (4, 8) to dot (4, 5). This line is also vertical. These two lines are parallel.
Set 3: Diagonal Parallel Lines
Let us draw diagonal lines with a slope of 1. This means for every 1 dot up, we go 1 dot right. Let us draw a line from dot (1, 5) to dot (4, 8). This line has a slope of 1. Now, let us draw another line from dot (3, 3) to dot (6, 6). This line also has a slope of 1. These two lines are parallel.
You can also see lines a, b, c, and d in the original diagram. They all have the same slope. So, lines a, b, c, and d form a set of parallel lines.
Answer
(i) Draw horizontal parallel lines by connecting dots in the same row. (ii) Draw vertical parallel lines by connecting dots in the same column. (iii) Draw diagonal parallel lines by keeping the "rise" and "run" the same for each line in the set.
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.]