Parallel and Intersecting Lines | IT

Question 14

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?

Solution

If two lines are parallel, then any transversal intersecting them will form equal corresponding angles.

Step 1 — Drawing a Transversal

Let us look at the given lines $l$ and $m$ . They appear to be parallel lines. Let us draw a line $t$ that cuts both lines $l$ and $m$ . This line $t$ is called a transversal.

Diagram 1

Step 2 — Identifying Corresponding Angles

When the transversal $t$ intersects lines $l$ and $m$ , it creates eight angles. Let us pick one pair of corresponding angles. For example, the angle above line $l$ and to the right of transversal $t$ . Let us call this angle $\angle 1$ . The corresponding angle is above line $m$ and to the right of transversal $t$ . Let us call this angle $\angle 2$ .

Diagram 2

Step 3 — Checking for Equality

The problem asks us to draw $t$ such that $\angle 1$ and $\angle 2$ are equal. If lines $l$ and $m$ are parallel, then $\angle 1$ will always be equal to $\angle 2$ . The diagram shows lines $l$ and $m$ as parallel. So, any transversal $t$ we draw will make corresponding angles equal. We can use a protractor to measure these angles. We will find that they are equal.

Answer

It is not hard to draw a transversal such that the corresponding angles are equal, because the lines $l$ and $m$ in Fig. 5.20 appear to be parallel. If the lines are parallel, any transversal will create equal corresponding angles.

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Q10

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Q11

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Q12

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Q13

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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

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Q17

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

Q18

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Q19

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

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