Parallel and Intersecting Lines | IT

Question 19

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

What causes these illusions?

Question diagram 1
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Solution

Optical illusions make our eyes and brain see things differently from how they truly are.

Step 1 — The central star illusion

Look at the top image. It has many lines. Some lines go straight up and down. These vertical lines are perfectly straight. They are also parallel to each other. The other lines spread out from the center. They look like spokes on a wheel. These spokes cross the vertical lines. This crossing confuses our brain. Our eyes think the vertical lines bend. But they are actually straight. This is an optical illusion. The central point draws our attention.

Diagram 1

Step 2 — The zigzag pattern illusion

Now look at the bottom-left image. It has a pattern of black shapes. These shapes are slanted. They look like zigzags. The white spaces are important. Look at the white horizontal lines. These white lines are perfectly straight. They are also parallel to each other. The bold black shapes trick our eyes. They make the white lines look tilted. Our brain sees the slanted black. It makes us think the white lines slant too. This is another optical illusion.

Diagram 2

Step 3 — The radiating lines illusion

Finally, look at the bottom-right image. It has two long horizontal lines. One is at the top. One is at the bottom. These two lines are perfectly straight. They are also parallel to each other. Many diagonal lines spread out. They come from a central point. These lines look like wheel spokes. They create a strong visual effect. This effect makes the horizontal lines curve. They seem to bend inward. Our brain interprets this as depth. But the lines are truly straight. This is a classic optical illusion.

Diagram 3

Answer

(a) In the top image, the vertical lines are actually parallel. The radiating lines crossing them create an optical illusion, making the vertical lines appear bent or not parallel. (b) In the bottom-left image, the horizontal white lines are actually parallel. The bold, slanted black shapes around them create an optical illusion, making the white lines appear tilted or zigzagging. (c) In the bottom-right image, the two long horizontal lines are actually parallel. The many diagonal lines radiating from the center create an optical illusion, making the horizontal lines appear to curve inward.

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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