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Class 9 The Fifth Postulate — practice questions with answers

Geometry — Foundations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Euclid's fifth postulate is also commonly known as the:
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Answer: A) Parallel postulate
Euclid's fifth postulate deals with parallel lines, so it is famously called the parallel postulate.
2. On the same side of a transversal, two interior angles are 95 deg and 88 deg. According to the fifth postulate, on which side do the lines meet?
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Answer: B) On the opposite side
On this side the sum is 95 + 88 = 183 deg, which is MORE than 180 deg. So the side whose interior angles sum to less than 180 deg (here 360 - 183 = 177 deg) is the opposite side. By the fifth postulate the lines meet on that opposite side.
3. If the fifth postulate is replaced so that MORE THAN ONE parallel line passes through an external point, the geometry is called:
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Answer: A) hyperbolic geometry
Allowing infinitely many parallels through a point gives hyperbolic (Lobachevskian) geometry.
4. Two lines AB and CD are cut by a transversal PQ. The interior angles on the right side measure 65 deg and 110 deg.
Find the difference (in degrees) between 180 deg and the sum of these two interior angles, and state whether the lines meet on the right.
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Answer: D) 5
Sum = 65 + 110 = 175 deg. Difference from 180 = 180 - 175 = 5 deg. Since the sum (175) is less than 180, the lines meet on the right side. The required difference is 5.
5. In the figure a transversal cuts two lines m and n. The co-interior angles on the right are 5z deg and 4z deg.
If it is given that the lines do NOT meet anywhere (they are parallel), find z and hence the value of 5z.
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Answer: D) 100
Parallel means co-interior sum = 180: 5z + 4z = 180, 9z = 180, z = 20. So 5z = 100 deg.
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