Parallel and Intersecting Lines | IT

Question 6

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.

Solution

We will observe how different line segments interact in the given figure.

Step 1 — Observing ST and UV

Segments ST and UV are shown. They appear to be parallel to each other. Parallel lines never meet.

Diagram 1

Step 2 — Observing AB and CD

Segments AB and CD cross each other. They meet at a single point. This point is called the intersection point. The segments intersect at point X.

Diagram 2

Step 3 — Observing PQ and OR

Segments PQ and OR are shown. They also appear to be parallel. Parallel lines do not cross.

Diagram 3

Step 4 — Observing Angle FGH

Segments FG and FH meet at point F. Point F is the vertex of the angle. The angle formed is $\angle \text{GFH}$ . Its measure is given.

$\text{Angle FGH} = \mathbf{115.3^\circ}$

$\boxed{\mathbf{115.3^\circ}}$

Diagram 4

Step 5 — Observing IL and MJ

Segments IL and MJ cross each other. They meet at a single point. This point is their intersection. The segments intersect at point Y.

Diagram 5

Answer

(i) Segments ST and UV are parallel. They do not meet or intersect. (ii) Segments AB and CD intersect at point X. (iii) Segments PQ and OR are parallel. They do not meet or intersect. (iv) Segments FG and FH meet at point F. They form an angle of $\mathbf{115.3^\circ}$ . (v) Segments IL and MJ intersect at point Y.

More questions in IT

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

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

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

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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 $t$ 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?

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 $l$ and $m$ parallel to each other?

Q18

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.

Q19

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

What causes these illusions?