Fig. 5.19 has a pair of parallel lines and (what is the notation used in the figure to indicate they are parallel?). Line is the transversal across these two lines. and are corresponding angles. Take a tracing paper and trace on it. Now place this tracing paper over and see if the angles align exactly. You will observe that the angles match. Check the other corresponding angles in the figure using a protractor. Are all the corresponding angles equal to each other?

Parallel and Intersecting Lines | A

Question 7

Fig. 5.19 has a pair of parallel lines $l$ and $m$ (what is the notation used in the figure to indicate they are parallel?). Line $t$ is the transversal across these two lines. $\angle a$ and $\angle b$ are corresponding angles. Take a tracing paper and trace $\angle a$ on it. Now place this tracing paper over $\angle b$ and see if the angles align exactly. You will observe that the angles match. Check the other corresponding angles in the figure using a protractor. Are all the corresponding angles equal to each other?

Solution

Understand the Question

When two parallel lines are intersected by a transversal, the angles occupying the same relative position at each intersection are called corresponding angles.
In geometric diagrams, parallel lines are denoted using arrowheads on the lines.
A fundamental geometric property is that if two parallel lines are cut by a transversal, every pair of corresponding angles is equal.

Step 1 · Identify Parallel Line Notation

Diagram 1

In the figure, arrowheads (arrows) drawn on lines $l$ and $m$ indicate that the lines are parallel ( $l \parallel m$ ).

Step 2 · Verify Angle Equality Using Tracing Paper

When $\angle a$ is traced on a sheet of tracing paper and superimposed on $\angle b$ , the two angles match and align exactly.

$\angle a = \angle b$

Step 3 · Measure Other Corresponding Angles

Measuring the remaining pairs of corresponding angles with a protractor confirms that each pair of corresponding angles has identical measure.

Answer

Notation: Arrowheads on lines $l$ and $m$ indicate they are parallel.

Observation: The angles align exactly, so $\angle a = \angle b$ .
Conclusion: Yes, all pairs of corresponding angles are equal to each other.

Common Mistakes

Angle Type Confusion: Confusing corresponding angles (angles in the same relative position at each intersection) with alternate interior angles (angles on opposite sides of the transversal between the two lines).
Assumption of Parallelism: Assuming corresponding angles are always equal. They are equal only when the two lines are parallel.

Question 7

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