- AMeet on that side
- BBe parallel
- CNever be drawn
- DMeet on the opposite side
Step-by-Step Solution
80 + 80 = 160 degrees < 180 degrees (two right angles), so the lines meet on that side per Postulate 5.
Answer: A) Meet on that side
If the two interior angles on the same side of a transversal are both 80 degrees, by Euclid's fifth postulate the two lines, if produced, will ____.
Class 9Introduction to Euclid's GeometryGeometry — Foundations
Key idea: The five postulates of Euclid
**Postulate 1**: A straight line may be drawn from any one point to any other point.
**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).
**Postulate 3**: A circle can be drawn with any centre and any radius.
**Postulate 4**: All right angles are equal to one another.
**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
These 5 statements are the seeds. Everything else in classical geometry grows from them.
**Postulate 2**: A terminated line (segment) can be produced indefinitely (extended).
**Postulate 3**: A circle can be drawn with any centre and any radius.
**Postulate 4**: All right angles are equal to one another.
**Postulate 5** (the famous one): If a straight line falling on two straight lines makes the interior angles on the same side together less than two right angles (180°), then the two lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
These 5 statements are the seeds. Everything else in classical geometry grows from them.
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