Constructions Quiz - ICSE Class 8 Mathematics
Free practice quiz: Constructions (ICSE Class 8 Mathematics). 39 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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To construct a perpendicular bisector of a given line segment AB, what is the minimum number of points required to define the arc used to intersect and form the perpendicular?
- 1
- 2
- 3
- 4
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Answer: B. 2
To construct a perpendicular bisector, we need to draw arcs from both endpoints of the line segment. Each arc is drawn with the compass point at an endpoint and a radius greater than half the length of the segment. Therefore, two distinct points (the endpoints of the segment) are used as centers for drawing these arcs.
Consider constructing a regular hexagon inscribed in a circle. What property of the hexagon and the circle is crucial for this construction?
- The radius of the circle is equal to the side length of the inscribed regular hexagon.
- The diameter of the circle is equal to the side length of the inscribed regular hexagon.
- The radius of the circle is half the side length of the inscribed regular hexagon.
- The diameter of the circle is half the side length of the inscribed regular hexagon.
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Answer: A. The radius of the circle is equal to the side length of the inscribed regular hexagon.
The key to constructing a regular hexagon inscribed in a circle is that the side length of the hexagon is equal to the radius of the circumscribing circle. This allows you to mark off six equal arcs around the circle using the compass set to the radius.
What is the primary function of the ruler in geometric constructions?
- To measure and draw arcs of circles.
- To draw lines and line segments of specific lengths.
- To measure and draw angles.
- To bisect angles and line segments.
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Answer: B. To draw lines and line segments of specific lengths.
The ruler (or straightedge) is used to draw straight lines and to mark specific lengths of line segments accurately. While it helps in defining points that create angles or segments, its primary role is in drawing straightness and measuring distance along a straight line.
If you are constructing an angle of 150 degrees using compass and straightedge, which of the following intermediate angles would be most useful?
- 90 degrees
- 120 degrees
- 75 degrees
- 180 degrees
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Answer: B. 120 degrees
One way to construct 150 degrees is to construct 180 degrees (a straight line), then construct a perpendicular to get 90 degrees. Bisecting the 60-degree angle adjacent to the 90-degree angle gives 30 degrees (90+30=120, not 150). A more direct method is to construct 120 degrees (by combining two 60-degree angles) and then add 30 degrees, which can be obtained by bisecting a 60-degree angle. Alternatively, construct 180 degrees and subtract 30 degrees.
To construct a square inscribed in a given circle, what property is used?
- The diagonals of the square are equal to the radius of the circle.
- The diagonals of the square bisect each other at right angles and are equal to the diameter of the circle.
- The sides of the square are equal to the radius of the circle.
- The diagonals of the square are equal to half the diameter of the circle.
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Answer: B. The diagonals of the square bisect each other at right angles and are equal to the diameter of the circle.
The diagonals of a square inscribed in a circle are diameters of the circle and are perpendicular bisectors of each other. By constructing two perpendicular diameters of the circle, their endpoints on the circle form the vertices of the inscribed square.