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First, look closely: The image displays four separate diagrams, labeled (i) through (iv). Each diagram shows two lines, labeled 'l' and 'm', intersected by a transversal line 'n'. In each case, two angles are marked with their degree measures. The task is to determine for which of these diagrams the lines 'l' and 'm' are parallel based on the given angle information.
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Next, find information: To solve this, I need to recall the geometric theorems that define when two lines are parallel based on the angles formed by a transversal. The key relationships are:
1. If corresponding angles are equal, the lines are parallel.
2. If alternate interior angles are equal, the lines are parallel.
3. If consecutive interior angles (same-side interior angles) are supplementary (add up to 180°), the lines are parallel.
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Then, review the findings: I will now analyze each diagram one by one using these rules.
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Diagram (i):
- The angles shown are 126° and 44°.
- These are consecutive interior angles (on the same side of the transversal, between the two lines).
- Their sum is 126° + 44° = 170°.
- Since 170° ≠ 180°, they are not supplementary.
- Therefore, lines 'l' and 'm' are
not parallel in diagram (i).
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Diagram (ii):
- The angles shown are 75° and 75°.
- These are alternate interior angles (on opposite sides of the transversal, between the two lines).
- Since both angles are equal (75° = 75°), the lines are parallel by the Alternate Interior Angles Theorem.
- Therefore, lines 'l' and 'm'
are parallel in diagram (ii).
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Diagram (iii):
- The angles shown are 123° and 57°.
- These are consecutive interior angles.
- Their sum is 123° + 57° = 180°.
- Since they are supplementary, the lines are parallel by the Consecutive Interior Angles Theorem.
- Therefore, lines 'l' and 'm'
are parallel in diagram (iii).
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Diagram (iv):
- The angles shown are 98° and 72°.
- These are consecutive interior angles.
- Their sum is 98° + 72° = 170°.
- Since 170° ≠ 180°, they are not supplementary.
- Therefore, lines 'l' and 'm' are
not parallel in diagram (iv).
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Based on the analysis, the lines 'l' and 'm' are parallel in diagrams (ii) and (iii).
(ii), (iii)
Parent Tip: Review the logic above to help your child master the concept of intersecting lines and angles worksheet.
