Solved Practical Geometry Multiple Choice Questions on Constructions and Figures
Practical Geometry is a critical part of the CBSE Class 8 syllabus. Students are often wary about this chapter as it involves a lot of geometrical concepts and constructions. However, a major chunk of questions from this topic comes in the form of MCQs. Therefore, by practicing more MCQ-type questions, the students will ensure securing better marks from this chapter. For the benefit of the students, we have a collection of all important Class 8 Math Chapter 4 Practical Geometry MCQs in the form of online downloadable material. We hope this resource will assist the students in preparing this particular topic. You can see a few examples in the next section regarding the type of questions one can expect.
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Practical Geometry MCQs - Solved Examples, and FAQs
The following is a compilation of CBSE Class 8 Math Chapter 4 Practical Geometry MCQs. All the examples given below have their solutions given underneath the question. These MCQs are very beneficial for the students, and practicing the likes of these will help the kids in acing their examination.
State the proper conditions under which one can construct a quadrilateral.
We are given one diagonal and the length of four sides.
We are given three sides and one diagonal.
When we have one diagonal and the measurement of two sides.
None of the above options.
Answer: a.
2. If you have the measure of two diagonals and the length of three sides given, which of the following is possible?
We can't construct a quadrilateral.
We can construct a quadrilateral.
We don't have enough information.
None of the above.
Answer: b.
3. We will require the measurements of two adjacent sides and how many angles, for proper construction of a quadrilateral?
Three
One
Two
All of the angles.
Answer: a.
4. We require the measurements of two diagonals and how many sides, for the proper construction of a quadrilateral?
One
Three
All four
Two
Answer: b.
5. If we have the measure of three sides, we need to know the value of ____ included angles to draw a quadrilateral.
One
Four
Three
Two
Answer: d.
6. For the geometrical construction of a square, we require which parameters?
The value of all interior angles.
The measure of all four sides.
The measure of one interior angle.
The measure of one side length.
Answer: d.
Elaboration: We know that in a square, the length of each side is equal, and all the internal angles measure 90°. Therefore, if we know the length of one side of a square, we have all the information to draw the square easily.
7. The parameters we need to know to draw a proper rectangle are:
The measure of each interior angle.
The length of each side.
The measure of one interior angle.
The length and breadth of the rectangle
Answer: d.
Elaboration: In a rectangle, the length of the parallel sides is the same. Also, every interior angle is 90°. Therefore, if we know the lengths and breadth, we have all the information to accurately draw the rectangle.
8. If we just have the measure of the diagonals for a quadrilateral, which one are we going to draw?
Kite
Parallelogram
Rhombus
Rectangle
Answer: c.
Elaboration: We can draw a rhombus with the measure of its diagonals because the rhombus has the unique property of its diagonals bisecting each other at 90°.
9. How many parameters must be available for us to draw a unique quadrilateral?
Three
Seven
Five
None of the above.
Answer: c.
10. For the proper construction of a parallelogram, the parameters required are
The length of two adjacent sides and two angles.
The length of two adjacent sides and one internal angle.
The measure of the parallel sides.
The measure of all internal angles.
Answer: b.
Elaboration: In a parallelogram, the parallel sides are equal. Therefore, knowing the measure of adjacent sides is synonymous with knowing the measure of each side. Also, the two angles in a parallelogram are supplementary to each other. Therefore, if we know one angle, we can find the other.
Fun Facts about Practical Geometry
Often students complain that Math and especially geometry is difficult and has no practical applications. To your surprise, geometry is one of the oldest subjects and it has a wide variety of practical applications. To prove this we have brought various interesting geometry facts for you:
Word “geometry” has Greek origins. “Geo” means earth and “metria” means measurement
Euclid is known as the Father of the geometry
Diagonal of a square bisect each other at 90 degrees and are perpendicular to each other
Evidence has been found which proves that ancient Egyptians used geometry and geometric equations.
Greeks used geometry in constructing their buildings. This shows how old and significant this subject is.
We have provided you with Practical Geometry MCQs - Solved Examples, and FAQs for free. All the questions are picked in such a way that they will facilitate your progress in geometry. All the questions have their answers given right beneath the questions themselves. You can find explanations on more such Mathematical topics on our website.
Conclusion
After going through this write-up you are well equipped to solve more advanced level questions based on Practical Geometry, more specifically on quadrilaterals. Even if you may not encounter many direct questions from the topic, you will be using this topic in solving other types of questions.
Solving these questions will also help you in tackling many questions in various entrance exams in the future that will have Mathematical or quantitative aptitude as a subject.
Thus covering this topic will not help you in scoring great marks in the upcoming exams but will also help you perform excellently in future exams as well.
FAQs on Practical Geometry MCQs with Answers and Solutions
1. What are Practical Geometry MCQs?
Practical Geometry MCQs are multiple-choice questions based on geometric constructions such as drawing lines, angles, triangles, and circles using a compass and ruler. These questions test conceptual understanding of constructions like:
- Constructing a perpendicular bisector
- Drawing an angle bisector
- Constructing triangles with given measurements
- Drawing parallel lines and circles
They are commonly asked in school exams and competitive tests to check both theoretical knowledge and practical geometry skills.
2. How do you construct the perpendicular bisector of a line segment?
The perpendicular bisector of a line segment is constructed by drawing equal arcs from both endpoints and joining their intersection points.
- Draw a line segment AB.
- With A as center and radius more than half of AB, draw arcs above and below the line.
- With B as center and same radius, draw arcs intersecting the previous arcs.
- Join the intersection points to get the perpendicular bisector.
This line divides AB into two equal parts and makes a 90° angle with it.
3. What is the correct method to construct an angle bisector?
An angle bisector divides an angle into two equal parts by using intersecting arcs inside the angle.
- Draw angle ∠ABC.
- With B as center, draw an arc cutting both arms at D and E.
- With D and E as centers and equal radius, draw arcs intersecting at F.
- Join B to F to get the angle bisector.
The two resulting angles are equal, each measuring half of the original angle.
4. How do you construct a triangle when three sides are given (SSS)?
A triangle can be constructed using the SSS (Side-Side-Side) rule by drawing arcs with given side lengths.
- Draw base AB equal to one given side.
- With A as center, draw an arc equal to the second side.
- With B as center, draw an arc equal to the third side.
- The arcs intersect at C; join AC and BC.
Triangle ABC formed satisfies all three given side lengths.
5. What is the difference between angle bisector and perpendicular bisector?
An angle bisector divides an angle into two equal angles, while a perpendicular bisector divides a line segment into two equal parts at 90°.
- Angle bisector: Works on angles and splits them equally.
- Perpendicular bisector: Works on line segments and forms a right angle.
Both are important constructions in practical geometry and are frequently tested in MCQs.
6. How do you construct a 60° angle using a compass?
A 60° angle is constructed by forming an equilateral triangle using equal arcs.
- Draw a line segment AB.
- With A as center and radius AB, draw an arc.
- With B as center and same radius, draw another arc intersecting at C.
- Join AC.
Angle ∠CAB = 60° because all sides of the equilateral triangle are equal.
7. What tools are required for practical geometry constructions?
The basic tools required for practical geometry are a compass, ruler (scale), and pencil.
- Compass: To draw arcs and circles
- Ruler: To draw straight lines
- Pencil: For accurate markings
A protractor is generally not used unless specifically required, as most constructions rely on compass techniques.
8. How do you construct a circle passing through three non-collinear points?
A circle through three non-collinear points is constructed by finding the intersection of the perpendicular bisectors of any two sides of the triangle formed.
- Join the three points to form a triangle.
- Construct perpendicular bisectors of any two sides.
- Their intersection is the circumcenter.
- With this center and radius equal to distance from center to any point, draw the circle.
This circle is called the circumcircle of the triangle.
9. What are common mistakes in Practical Geometry MCQs?
Common mistakes in Practical Geometry MCQs include using incorrect radius lengths and misunderstanding construction steps.
- Not keeping the same radius while drawing intersecting arcs
- Confusing angle bisector with perpendicular bisector
- Choosing wrong triangle construction rule (SSS, SAS, ASA)
- Ignoring given measurements
Carefully following each construction step reduces errors in objective-type questions.
10. How do you construct a triangle when two sides and the included angle are given (SAS)?
A triangle can be constructed using the SAS (Side-Angle-Side) rule by first drawing the included angle and then marking the given sides.
- Draw one side AB.
- At A, construct the given angle.
- On the angle arm, mark length equal to the second side.
- Join the marked point to B.
The resulting triangle satisfies the two given sides and the included angle exactly.
