Chapter 5 Parallel and Intersecting Lines (Class 7 - Latest Maths NCERT (Ganita Prakash I) NCERT Solutions)

Question. Can two straight lines intersect at more than one point?

Question. Draw two lines on a plain sheet of paper so that they intersect. Measure the four angles formed with a protractor. Draw four such pairs of intersecting lines and measure the angles formed at the points of intersection.

What patterns do you observe among these angles?

Question. When two lines intersect each other and form four angles, labelled $a$, $b$, $c$ and $d$, as in Fig. 5.2, then $\angle a$ and $\angle c$ are equal, and $\angle b$ and $\angle d$ are equal!

Is this always true for any pair of intersecting lines?

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

Question. Which pairs of lines appear to be parallel in Fig. 5.6 below?

Question. Take a plain square sheet of paper (use a newspaper for this activity).

• How would you describe the opposite edges of the sheet? They are _________________________ to each other.

• How would you describe the adjacent edges of the sheet? The adjacent edges are _________________________ to each other. They meet at a point. They form right angles.

• Fold the sheet horizontally in half. A new line is formed (see Fig. 5.7).

• How many parallel lines do you see now? How does the new line segment relate to the vertical sides?

• Make one more horizontal fold in the folded sheet. How many parallel lines do you see now?

• What will happen if you do it once more? How many parallel lines will you get? Is there a pattern? Check if the pattern extends further, if you make another horizontal fold.

• Make a vertical fold in the square sheet. This new vertical line is ___________ to the previous horizontal lines.

• Fold the sheet along a diagonal. Can you find a fold that creates a line parallel to the diagonal line?

Question. Here is another activity for you to try.

• Take a square sheet of paper, fold it in the middle and unfold it.

• Fold the edges towards the centre line and unfold them.

• Fold the top right and bottom left corners onto the creased line to create triangles. Refer to Fig. 5.8.

• The triangles should not cross the crease lines.

• Are $a, b$ and $c$ parallel to $p, q$ and $r$ respectively? Why or why not?

Question 1. Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.

Question 2. 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?

Question 3. 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.

Question 4. 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?

Question 5. In Fig. 5.13, which line is parallel to line $a$ —– line $b$ or line $c$? How do you decide this?

Question. In Fig. 5.14, line $t$ intersects lines $l$ and $m$. $t$ is called a transversal.

Notice that $8$ angles are formed when a line crosses a pair of lines.

Is it possible for all the eight angles to have different measurements? Why, why not?

Question. What about five different angles — $6, 5, 4, 3$ and $2$?

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

Question. We know how to fold a piece of paper to get a line perpendicular to $l$. Now, try to fold a perpendicular to $l$ such that it passes through point $A$. Let us call this new crease $t$.

Now, fold a line perpendicular to $t$ passing through $A$ again. Let us call this line $m$. The lines $l$ and $m$ are parallel to each other.

Why are lines $l$ and $m$ parallel to each other?

Question 1. Find the angles marked below.

Question 2. Find the angle represented by $a$.

Question 3. In the figures below, what angles do $x$ and $y$ stand for?

Question 4. In Fig. 5.33, $\angle ABC = 45^\circ$ and $\angle IKJ = 78^\circ$. Find angles $\angle GEH, \angle HEF, \angle FED$

Question 5. In Fig. 5.34, $AB$ is parallel to $CD$ and $CD$ is parallel to $EF$. Also, $EA$ is perpendicular to $AB$. If $\angle BEF = 55^\circ$, find the values of $x$ and $y$.

Question 6. What is the measure of angle $\angle NOP$ in Fig. 5.35?

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