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.

This ICSE Class 8 Mathematics practice quiz has 39 multiple-choice questions on Constructions, and 39 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. 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. 1
   2. 2
   3. 3
   4. 4
   Show answer

   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.

2. Consider constructing a regular hexagon inscribed in a circle. What property of the hexagon and the circle is crucial for this construction?

   1. The radius of the circle is equal to the side length of the inscribed regular hexagon.
   2. The diameter of the circle is equal to the side length of the inscribed regular hexagon.
   3. The radius of the circle is half the side length of the inscribed regular hexagon.
   4. The diameter of the circle is half the side length of the inscribed regular hexagon.
   Show answer

   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.

3. What is the primary function of the ruler in geometric constructions?

   1. To measure and draw arcs of circles.
   2. To draw lines and line segments of specific lengths.
   3. To measure and draw angles.
   4. To bisect angles and line segments.
   Show answer

   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.

4. If you are constructing an angle of 150 degrees using compass and straightedge, which of the following intermediate angles would be most useful?

   1. 90 degrees
   2. 120 degrees
   3. 75 degrees
   4. 180 degrees
   Show answer

   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.

5. To construct a square inscribed in a given circle, what property is used?

   1. The diagonals of the square are equal to the radius of the circle.
   2. The diagonals of the square bisect each other at right angles and are equal to the diameter of the circle.
   3. The sides of the square are equal to the radius of the circle.
   4. The diagonals of the square are equal to half the diameter of the circle.
   Show answer

   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.

More questions in this quiz

Answers and explanations are in the full quiz.

1. When constructing an angle bisector of a given angle ∠ABC, the first step typically involves placing the compass point at B and drawing an arc that intersects both rays BA and BC at points P and Q respectively. What is the primary purpose of this initial arc?
2. You are constructing a perpendicular from a point P not on a line L. What is the first step in this construction?
3. If you are constructing a circle with a given radius, what is the role of the compass?
4. In the construction of a triangle, when given three sides (SSS criterion), what is the first step usually involving the compass?
5. Which construction is NOT typically performed using a compass and straightedge?
6. To construct a square with a given side length 's', after drawing the side, what is the next logical step in a compass and straightedge construction?
7. When constructing an isosceles triangle with two equal sides of length 'a' and a base of length 'b', how many arcs are typically needed to locate the apex (the vertex opposite the base)?
8. In the construction of a 30-60-90 triangle using compass and straightedge, what is the relationship between the initial angle constructed and the final angles?
9. What is the minimum number of compass settings required to construct a triangle congruent to a given triangle using the SSS criterion?
10. To construct a circle that passes through three non-collinear points A, B, and C, what geometrical concept do you primarily rely on?
11. In constructing a line parallel to a given line through a point not on the line, a common method involves using equal alternate interior angles. What is the prerequisite construction for creating these equal angles?
12. Which of the following compass and straightedge constructions would result in an angle of 45 degrees?
13. When constructing a tangent to a circle from an external point P, the first crucial step involves the circle's center (O) and the external point (P). What is this step?
14. When constructing an angle equal to a given angle, which step involves transferring the angle's measure accurately?
15. To construct a perpendicular from a point P ON a line L, what is the first step?
16. Which of the following constructions is based on the property that the locus of points equidistant from two intersecting lines is the angle bisector of the angles formed by these lines?
17. In constructing a rhombus with a given side length 's' and a given angle 'θ', what is the sequence of steps?
18. What tool is used to accurately set and transfer lengths during geometric constructions?
19. Which of the following is the most accurate description of the purpose of an angle bisector construction?
20. What is the primary role of a set square in geometric constructions?
21. When constructing a perpendicular bisector of a line segment AB, the arcs drawn from A and B must have:
22. To construct a triangle ABC with BC = 5 cm, AB = 7 cm, and AC = 8 cm, the first step should be:
23. In constructing an equilateral triangle, what is the angle measure of each interior angle?
24. When constructing a line parallel to a given line through a point, using the property of corresponding angles, what is the basic construction required?
25. What is the primary tool for measuring and drawing angles in geometric constructions?
26. When constructing a triangle given two sides and the included angle (SAS), after drawing one side, what is the next step?
27. What is the geometrical meaning of the intersection of the angle bisectors of a triangle?
28. Which of the following is a necessary step when constructing a perpendicular to a line segment at its midpoint?
29. Which of the following angle constructions is NOT possible with standard compass and straightedge techniques if starting from basic angles like 180, 90, 60?
30. To construct a rectangle with a given length 'l' and width 'w', after drawing the length, what is the subsequent step?
31. In the construction of a regular pentagon inscribed in a circle, what is the approximate angle subtended by each side at the center of the circle?
32. When constructing a tangent to a circle from an external point P, what property of the point of tangency (T) is used with respect to the radius OT?
33. To construct a triangle congruent to a given triangle ABC using the SAS (Side-Angle-Side) criterion, what is the minimum number of angle measurements required?
34. What tool is primarily used to ensure accuracy in transferring angles and setting radii for arcs in geometric constructions?

More quizzes

• Cubes and Cube Roots▶ Play
• Data Handling (Graphs, Pie Charts, Histograms)▶ Play
• Exponents and Powers▶ Play
• Geometry – Understanding Shapes▶ Play
• Linear Equations and Linear Inequations▶ Play
• Mensuration – Perimeter, Area, Surface Area, Volume & Capacity▶ Play

Browse all Mathematics quizzes

More to play