Question 3
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?
We can use the grid lines to help us identify parallel and perpendicular lines in the given figure.
Step 1 — Spotting Perpendicular Lines
Perpendicular lines meet each other at a perfect right angle. A right angle measures 90 degrees.
We look for lines that form a square corner. On a grid, this means one line segment is perfectly horizontal. The other line segment is perfectly vertical. They meet at a grid intersection point. We mark this intersection with a small square symbol. This square symbol shows a 90-degree angle.
Step 2 — Spotting Parallel Lines
Parallel lines are lines that always stay the same distance apart. They never meet, no matter how far we extend them.
We look for lines that run in the exact same direction. On a grid, horizontal lines are parallel to other horizontal lines. Vertical lines are parallel to other vertical lines. Diagonal lines are parallel if they have the same slope. This means they go up/down the same number of squares for the same number of squares across. We mark parallel lines with arrows on them. Lines with one arrow are parallel to other lines with one arrow. Lines with two arrows are parallel to other lines with two arrows.
Answer
(a) We spot perpendicular lines by looking for lines that meet to form a 90-degree angle. On a grid, these lines often run perfectly horizontally and vertically, forming a perfect square corner. (b) We spot parallel lines by looking for lines that always stay the same distance apart. They never meet, even if we extend them very far in either direction. On a grid, these lines run in the exact same direction.
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.]