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

Understand the Question

When two parallel lines are intersected by a straight line called a transversal, the pairs of corresponding angles formed are always equal.
If the given lines $l$ and $m$ are parallel, any transversal drawn across them naturally produces equal corresponding angles, making the task straightforward.

Step 1 · Draw a Transversal

Draw a line $t$ that intersects both given lines $l$ and $m$ . Diagram 1

Line $t$ is a transversal to lines $l$ and $m$ .

Step 2 · Identify Corresponding Angles

When transversal $t$ intersects lines $l$ and $m$ , choose a pair of corresponding angles:

Let $\angle 1$ be the angle in the upper-right position at line $l$ .
Let $\angle 2$ be the angle in the upper-right position at line $m$ .

Step 3 · Measure and Verify Equality

Since lines $l$ and $m$ are parallel, the corresponding angles are equal: $\angle 1 = \angle 2$

Measuring with a protractor confirms that $\angle 1 = \angle 2$ holds for any transversal drawn across parallel lines.

Answer

No, it is not hard, because lines $l$ and $m$ are parallel. Any transversal drawn across parallel lines automatically forms equal corresponding angles.

Common Mistakes

Non-Parallel Assumption: Assuming that corresponding angles are only equal for a specific transversal orientation; in reality, if lines are parallel, any transversal creates equal corresponding angles.
Misidentifying Angle Pairs: Confusing corresponding angles (matching corner positions) with alternate interior or co-interior angles.

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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?