Class 9 Constructions of Triangles — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. Which instrument is used to draw arcs of a given radius during a triangle construction?
ACompass
BProtractor
CSet square
DDivider
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Answer: A) Compass
A compass is used to draw arcs and circles of a fixed radius, which is essential for marking equal lengths and constructing angles in geometric constructions.
2. To construct a 120 deg angle with a compass, how many successive 60 deg arc steps of equal radius are marked along the main arc?
A3
B2
C4
D1
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Answer: B) 2
Marking two consecutive equal-radius steps (each spanning 60 deg) along the arc from the starting point gives 60 + 60 = 120 deg.
3. When you construct the perpendicular bisector of side DC to locate vertex A (in the sum-of-sides construction), the key property used is that every point on it is:
Aequidistant from D and C
Bequidistant from B and C
Con side BC
Dthe midpoint of BD
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Answer: A) equidistant from D and C
A point on the perpendicular bisector of DC is equidistant from D and C. Choosing A on it gives AD = AC, which makes the side lengths come out correctly.
4. Constructing a triangle from perimeter 13 cm with base angles 45 deg and 60 deg uses the perpendicular bisectors of two slanted segments to find the actual base ends. The third angle of the finished triangle is:
A75
B67
C83
D150
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Answer: A) 75
Third angle = 180 - 45 - 60 = 75 deg.
5. A student must construct triangle ABC with base BC = 7 cm, base angle B = 45 deg and AB + AC = 6 cm. Why is this construction impossible?
ABecause AB + AC = 6 cm is less than the base BC = 7 cm
BBecause angle B is too small
CBecause 6 cm is even
DBecause the base must be 6 cm
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Answer: A) Because AB + AC = 6 cm is less than the base BC = 7 cm
The sum of the other two sides must be greater than the base (triangle inequality). Since 6 < 7, no triangle exists, so the construction cannot be done.