Question 19

Context: Let us observe what happens when two lines intersect.

Q. How many angles do they form?

Can two straight lines intersect at more than one point?

In Fig. 5.2, if $\angle a$ is $120^\circ$, can you figure out the measurements of $\angle b$, $\angle c$ and $\angle d$, without drawing and measuring them?

Context: When two lines intersect each other and form four angles, labelled $a$, $b$, $c$ and $d$, then $\angle a$ and $\angle c$ are equal, and $\angle b$ and $\angle d$ are equal.

Q. Is this always true for any pair of intersecting lines?

Can you draw a pair of intersecting lines such that all four angles are equal? Can you figure out what will be the measure of each angle?

Observe Fig. 5.5 and describe the way the line segments meet or cross each other in each case, with appropriate mathematical words (a point, an endpoint, the midpoint, meet, intersect) and the degree measure of each angle.

Are line segments $\text{ST}$ and $\text{UV}$ likely to meet if they are extended?

Are line segments $\text{OP}$ and $\text{QR}$ likely to meet if they are extended?

Name some parallel lines you can spot in your classroom.

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

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

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

Suppose, we have a transversal intersecting two parallel lines. What can be said about the corresponding angles?

Context: Activity 5 In Fig. 5.20, draw a transversal $t$ to the lines $l$ and $m$ such that one pair of corresponding angles is equal. You can measure the angles with a protractor.

Q. Are you finding it hard to draw a transversal such that the corresponding angles are equal?

Draw two more parallel lines using the long side of the set square as shown in Fig. 5.22. How do you know these two lines are parallel? Can you check if the corresponding angles are equal?

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

Is there a relation between $\angle 3$ and $\angle 6$? You could try to find the relationship by taking different values for $\angle 3$ and see what $\angle 6$ is. Once you find a relation, try to justify it or prove that this relation holds always.