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All questions of Practical Geometry for Class 6 Exam

Which geometrical instrument used to draw and measure angles?
  • a)
    Protractor
  • b)
    Set squares
  • c)
    Divider
  • d)
    Compasses
Correct answer is 'D'. Can you explain this answer?

Shilpa Shah answered
Protractor

A protractor is a geometrical instrument that is used to draw and measure angles. It is a semi-circular tool made of plastic or metal and has a degree scale from 0 to 180 degrees. Protractors are commonly used in geometry, trigonometry, and other mathematical fields to measure angles and draw precise angles.

Uses of Protractor

Protractors have many uses, including:

- Measuring angles: A protractor can be used to determine the size of an angle, which is measured in degrees. It is placed on the angle so that one of its arms coincides with one side of the angle, and the other arm points to the other side of the angle. The degree scale on the protractor can then be read to determine the size of the angle.

- Drawing angles: A protractor can also be used to draw precise angles. The center of the protractor is placed on the vertex of the angle, and one of its arms is aligned with one side of the angle. The desired angle can then be drawn by tracing along the edge of the protractor.

Advantages of Protractor

The advantages of using a protractor include:

- Precision: A protractor allows precise measurement and drawing of angles, making it an essential tool in many fields.

- Easy to use: Protractors are easy to use and can be used by anyone, including students, teachers, and professionals.

- Versatile: Protractors can be used in various applications, including construction, engineering, and design.

Conclusion

In conclusion, a protractor is an essential geometrical instrument used to draw and measure angles accurately. It is a versatile tool that can be used in many fields, including mathematics, engineering, and design.

Which geometrical instrument used to draw perpendicular and parallel lines?
  • a)
    Divider
  • b)
    Compasses
  • c)
    Ruler
  • d)
    Set squares
Correct answer is option 'D'. Can you explain this answer?

Bibek Verma answered
Set squares are used to draw perpendicular and parallel lines

Set squares are the geometrical instruments that are used to draw perpendicular and parallel lines.


  • Perpendicular lines: Set squares are used to draw perpendicular lines. They are made up of two straight edges, one of which is fixed at right angles to the other. When the fixed edge is placed on a line, the other edge can be used to draw a perpendicular line.

  • Parallel lines: Set squares are also used to draw parallel lines. By placing the fixed edge of the set square parallel to the line to be copied, the other edge can be used to draw a line parallel to it.



Other geometrical instruments and their uses

Other geometrical instruments that are commonly used are:


  • Divider: Dividers are used to measure and transfer distances between two points.

  • Compasses: Compasses are used to draw circles and arcs.

  • Ruler: A ruler is used to draw straight lines and measure lengths.



However, none of these instruments can be used to draw perpendicular or parallel lines as accurately as set squares. Therefore, when it comes to drawing perpendicular or parallel lines, set squares are the best option.

A line has ___________ length.
  • a)
    definite
  • b)
    no
  • c)
    indefinite
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Rutuja Roy answered
**Explanation:**

A line is a one-dimensional geometric figure that extends infinitely in both directions. It is made up of an infinite number of points that are all equidistant from each other. Since a line extends infinitely, it does not have a definite or measurable length.

**Infinite Length:**

- A line has an infinite length because it has no endpoints and continues indefinitely in both directions.
- No matter how far you extend a line, you can always extend it further without reaching an endpoint.
- This infinite nature of a line makes it impossible to assign a definite or measurable length to it.

**Comparison to Line Segments:**

- It is important to note the difference between a line and a line segment.
- A line segment is a portion of a line that has two distinct endpoints.
- Unlike a line, a line segment has a definite and measurable length because it has endpoints that mark its boundaries.

**Mathematical Representation:**

- In mathematics, a line can be represented by a lowercase letter with an arrow on top (∞).
- This symbol indicates that the line extends infinitely in both directions.

**Conclusion:**

- In conclusion, a line does not have a definite length because it extends infinitely in both directions.
- It is an infinite geometric figure made up of an infinite number of points.
- The length of a line is considered indefinite, as it cannot be measured or assigned a specific value.

Number of circles passing through a given point are ____.
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    infinite
Correct answer is option 'D'. Can you explain this answer?

Nilanjan Unni answered
Explanation:

A circle is defined as a set of all points in a plane that are at a given distance from a given point, called the center of the circle.

When a point is given, there are infinite circles that could pass through that point. This is because a circle is defined by its center and radius, and there are infinite points that could serve as the center of a circle passing through the given point.

For example, consider a point P in a plane. We can draw a circle with center P and any positive radius r, and that circle will pass through P. We can also draw a circle with center Q, where Q is any point on the perpendicular bisector of the line segment between P and any other point in the plane, and that circle will also pass through P.

Therefore, the correct answer is option D, infinite.

Two lines are said to be perpendicular to each other when they meet at ____angle.
  • a)
    180
  • b)
    90 
  • c)
    60
  • d)
    360
Correct answer is option 'B'. Can you explain this answer?

Perpendicular Lines

Perpendicular lines are an important concept in geometry. They are two lines that intersect each other at a right angle, which is 90 degrees. Perpendicular lines are often used in architecture and engineering, as they help create stable structures and accurate measurements.

Definition

Perpendicular lines are two lines that meet at a right angle. This means that the angle formed by the intersection of the two lines is exactly 90 degrees. When two lines are perpendicular, they are said to be orthogonal.

Properties

Perpendicular lines have several important properties:

- The slopes of the two lines are negative reciprocals of each other. This means that if one line has a slope of m, the other line will have a slope of -1/m.
- The product of the slopes of two perpendicular lines is -1.
- If two lines are perpendicular, they will form four right angles at their intersection.

Examples

Here are some examples of perpendicular lines:

- The x-axis and y-axis on a coordinate plane are perpendicular.
- The sides of a square are all perpendicular to each other.
- The legs of a right triangle are perpendicular to each other.

Conclusion

Perpendicular lines are an important concept in geometry that can be found in many different areas of math and science. They are two lines that intersect at a right angle, and they have several important properties that make them useful in a variety of applications.

How do you draw a 90∘ angle?
  • a)
    By drawing a perpendicular to a line from a point lying on it.
  • b)
    By bisecting a 120∘ angle.
  • c)
    By bisecting a 60 angle.
  • d)
    By drawing multiples of 45 angle.
Correct answer is option 'A'. Can you explain this answer?

Shreyshi answered
Two lines that intersect each other and formed the angle of 90degree are called Perpendicular line.
In this question, we have to draw a angle of 90 degree so when we draw a perpendicular line the angle of 90 degree will formed.
So, Option A is the correct answer.

Name the geometrical instrument having a pair – a pointer on one end and a pencil on the other.
  • a)
    Set squares
  • b)
    Divider
  • c)
    Protractor
  • d)
    Compasses
Correct answer is option 'D'. Can you explain this answer?

Gayatri Chavan answered
A pair of compasses, also known as a compass, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, they can also be used as tools to measure distances, in particular on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.

Which of the following is done to draw an angle of 150 using compasses and a ruler?
  • a)
    Bisecting 120 and 180 angles.
  • b)
    Bisecting 60 and 120 angles.
  • c)
    Bisecting 0 and 60 angles.
  • d)
    Bisecting a 360 angle.
Correct answer is option 'A'. Can you explain this answer?

Anisha Iyer answered
To draw an angle of 150° using compasses and a ruler, we need to follow the process of bisecting a 120° and 180° angle.

Here is a step-by-step explanation of how to draw an angle of 150° using compasses and a ruler:

1. Draw a line segment AB using a ruler.
2. Place the compasses on point A and draw an arc that intersects AB.
3. Without changing the compasses' width, place the compasses on point B and draw another arc that intersects the first arc.
4. Label the point where the two arcs intersect as C.
5. Place the compasses on point C and draw an arc that intersects the first arc.
6. Without changing the compasses' width, place the compasses on point B and draw another arc that intersects the second arc.
7. Label the point where the two arcs intersect as D.
8. Draw a line segment CD using a ruler.
9. Label the point of intersection between AB and CD as E.

Now, we have created a 120° angle ACE.

10. Place the compasses on point E and draw an arc that intersects AB.
11. Without changing the compasses' width, place the compasses on point A and draw another arc that intersects the first arc.
12. Label the point where the two arcs intersect as F.
13. Draw a line segment EF using a ruler.

Now, we have bisected the 120° angle ACE into two equal angles, which are each 60°. The angle EAF is 60°.

14. Place the compasses on point E and draw an arc that intersects CD.
15. Without changing the compasses' width, place the compasses on point D and draw another arc that intersects the first arc.
16. Label the point where the two arcs intersect as G.
17. Draw a line segment EG using a ruler.

Now, we have bisected the 60° angle EAF into two equal angles, which are each 30°. The angle EAG is 30°.

18. Place the compasses on point E and draw an arc that intersects AB.
19. Without changing the compasses' width, place the compasses on point A and draw another arc that intersects the first arc.
20. Label the point where the two arcs intersect as H.
21. Draw a line segment EH using a ruler.

Now, we have bisected the 30° angle EAG into two equal angles, which are each 15°. The angle EAH is 15°.

22. Measure the angle EAH using a protractor, and it will measure 15°.

Therefore, by bisecting a 120° angle and then bisecting the resulting 60° angle, we can construct an angle of 150° using compasses and a ruler.

Which geometrical instrument used to draw and measure angles?
  • a)
    Protractor
  • b)
    Set squares
  • c)
    Divider
  • d)
    Compasses
Correct answer is option 'D'. Can you explain this answer?

Gayatri Chavan answered
A protractor is a measuring instrument, typically made of transparent plastic or glass, for measuring angles. Most protractors measure angles in degrees . 

Identify the instruments used to bisect a given line segment.
  • a)
    A scale and a protractor
  • b)
    Scale and compasses
  • c)
    Scale and setsquares
  • d)
    A scale
Correct answer is option 'B'. Can you explain this answer?

Ananya Das answered
Using Scale and Compasses to Bisect a Line Segment:

Step 1:
Place the scale on the line segment that needs to be bisected.

Step 2:
Use the compasses to measure the length of the line segment.

Step 3:
Place the compasses at one end of the line segment and draw an arc that intersects the line.

Step 4:
Without changing the compass width, place the compasses at the other end of the line segment and draw another arc that intersects the first arc.

Step 5:
Draw a line connecting the intersection points of the two arcs. This line will bisect the original line segment.
Using a scale and compasses is the most accurate method for bisecting a line segment as it involves precise measurements and construction techniques. This combination allows for the creation of a perpendicular line that divides the line segment into two equal parts.

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