Parallel and Intersecting Lines | IT

Question 7

Are line segments ST and UV likely to meet if they are extended?

Question diagram 1
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Solution

Lines that are not parallel will always cross each other if we extend them.

Step 1 — Understand parallel and intersecting lines

Let us think about lines. Parallel lines are lines that always stay the same distance apart. They never meet, no matter how far we extend them. Intersecting lines are lines that cross at one point. These lines are not parallel.

Diagram 1

Step 2 — Examine line segments ST and UV

Let us look at the line segments ST and UV in the diagram. We need to see if they look parallel. If they were parallel, the distance between them would stay the same. We can see that the line segment ST and UV do not look perfectly parallel. The direction of ST seems slightly different from the direction of UV. If we imagine extending these lines, they would not stay the same distance apart. So, they are not parallel lines.

Diagram 2

Answer

Line segments ST and UV are likely to meet if they are extended. This is because they are not parallel.

More questions in IT

Q1

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

Q. How many angles do they form?

Q2

Can two straight lines intersect at more than one point?

Q3

In Fig. 5.2, if a\angle a is 120120^\circ, can you figure out the measurements of b\angle b, c\angle c and d\angle d, without drawing and measuring them?

Q4

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

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

Q5

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?

Q6

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.

Q7

Are line segments ST and UV likely to meet if they are extended?

Q8

Are line segments OP and QR likely to meet if they are extended?

Q9

Name some parallel lines you can spot in your classroom.

Q10

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

Q11

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

Q12

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

Q13

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

Q14

Context: Activity 5 In Fig. 5.20, draw a transversal tt to the lines ll and mm 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?

Q15

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?

Q17

Why are lines ll and mm parallel to each other?

Q18

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

Q19

There do not seem to be any parallel lines here. Or, are there?

What causes these illusions?

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