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All questions of Constructions for Class 8 Exam
What method is used to construct a rectangle when two adjacent sides are known?- a)Drawing the length and using arcs for the width
- b)Using diagonals to find the corners
- c)Measuring the angles with a protractor
- d)Drawing one side and constructing a 90° angle
Correct answer is option 'D'. Can you explain this answer?
What method is used to construct a rectangle when two adjacent sides are known?
a)
Drawing the length and using arcs for the width
b)
Using diagonals to find the corners
c)
Measuring the angles with a protractor
d)
Drawing one side and constructing a 90° angle
 | Shivani Khanna answered |
Understanding Rectangle Construction
To construct a rectangle when two adjacent sides are known, option 'D' is indeed the correct method. Here’s why:
Step 1: Drawing One Side
- Begin by drawing one of the known sides on your drawing surface. Let's say this side is the length of the rectangle.
Step 2: Constructing a 90° Angle
- At one end of the drawn side, you need to form a right angle (90°). This can be done using a set square, or by employing a compass to create arcs that intersect at right angles.
- The construction of a 90° angle is crucial because rectangles require all interior angles to be right angles.
Step 3: Measuring the Adjacent Side
- From the point where the right angle is formed, measure out the length of the adjacent side (width of the rectangle) along the line created by the 90° angle.
Step 4: Completing the Rectangle
- Repeat the process at the other end of the original side, drawing another 90° angle and measuring out the adjacent side.
- Finally, connect the ends of these two lines to complete the rectangle.
Key Takeaways
- Constructing a rectangle fundamentally relies on the ability to create and measure right angles.
- This method ensures that all angles are precisely 90°, which is essential for the shape to be classified as a rectangle.
By following these steps, you can effectively and accurately construct a rectangle using the known lengths of two adjacent sides.
To construct a rectangle when two adjacent sides are known, option 'D' is indeed the correct method. Here’s why:
Step 1: Drawing One Side
- Begin by drawing one of the known sides on your drawing surface. Let's say this side is the length of the rectangle.
Step 2: Constructing a 90° Angle
- At one end of the drawn side, you need to form a right angle (90°). This can be done using a set square, or by employing a compass to create arcs that intersect at right angles.
- The construction of a 90° angle is crucial because rectangles require all interior angles to be right angles.
Step 3: Measuring the Adjacent Side
- From the point where the right angle is formed, measure out the length of the adjacent side (width of the rectangle) along the line created by the 90° angle.
Step 4: Completing the Rectangle
- Repeat the process at the other end of the original side, drawing another 90° angle and measuring out the adjacent side.
- Finally, connect the ends of these two lines to complete the rectangle.
Key Takeaways
- Constructing a rectangle fundamentally relies on the ability to create and measure right angles.
- This method ensures that all angles are precisely 90°, which is essential for the shape to be classified as a rectangle.
By following these steps, you can effectively and accurately construct a rectangle using the known lengths of two adjacent sides.
How can parallel lines be constructed through a given point?- a)Drawing a line at a measured distance
- b)Using a right angle to find the direction
- c)Constructing equal angles at the point
- d)By measuring the angle at the point
Correct answer is option 'C'. Can you explain this answer?
How can parallel lines be constructed through a given point?
a)
Drawing a line at a measured distance
b)
Using a right angle to find the direction
c)
Constructing equal angles at the point
d)
By measuring the angle at the point
 | Trisha Vashisht answered |
To construct a line parallel to a given line through a specific point, you first join the point to any point on the given line. Then, you construct an angle at the given point that is equal to the angle formed at the point on the line. Extending the arm of this angle creates a parallel line. This method highlights the concept of alternate angles and their properties in parallel line constructions.
How do you construct a square when one side is given?- a)Drawing one side and constructing a 90° angle
- b)Applying the Pythagorean theorem
- c)Drawing a line segment and constructing equal angles
- d)Using a diagonal to find the other corners
Correct answer is option 'A'. Can you explain this answer?
How do you construct a square when one side is given?
a)
Drawing one side and constructing a 90° angle
b)
Applying the Pythagorean theorem
c)
Drawing a line segment and constructing equal angles
d)
Using a diagonal to find the other corners
| | Trisha Vashisht answered |
To construct a square when one side is given, start by drawing the given side. At one endpoint, you construct a 90° angle, marking the second side. Finally, by using the same length as the first side, you can find the other vertices of the square using arcs. This process illustrates how squares are defined by equal sides and right angles.
What is the method for constructing a diagonal in a rectangle when one side is known?- a)Constructing a 90° angle at one endpoint
- b)Drawing arcs to find the other side
- c)Using the length of the diagonal
- d)Drawing the opposite side first
Correct answer is option 'A'. Can you explain this answer?
What is the method for constructing a diagonal in a rectangle when one side is known?
a)
Constructing a 90° angle at one endpoint
b)
Drawing arcs to find the other side
c)
Using the length of the diagonal
d)
Drawing the opposite side first
 | EduRev Class 8 answered |
To construct a diagonal in a rectangle when one side is known, you first draw the side. At one endpoint, you create a 90° angle to establish the second side. Once you have the dimensions of the rectangle, the diagonal can be easily drawn by connecting the opposite corners. This method reinforces understanding the relationships in rectangles, including how the diagonals bisect each other.
What is the construction technique to create a rectangle when one side and one diagonal are given?- a)Drawing arcs to find the other sides
- b)Measuring angles with a protractor
- c)Constructing a right angle at one endpoint
- d)Using the diagonal to find the rectangle's dimensions
Correct answer is option 'C'. Can you explain this answer?
What is the construction technique to create a rectangle when one side and one diagonal are given?
a)
Drawing arcs to find the other sides
b)
Measuring angles with a protractor
c)
Constructing a right angle at one endpoint
d)
Using the diagonal to find the rectangle's dimensions
| | Trisha Vashisht answered |
When constructing a rectangle with one side and one diagonal known, you start by drawing the given side. At one endpoint, you create a right angle, and then from the other endpoint, you draw an arc using the length of the diagonal to intersect the line at the right angle. This intersection helps determine the other vertices of the rectangle. This method emphasizes the relationships between sides and diagonals in rectangular constructions.
What is the procedure for constructing a 60° angle using a ruler and compass?- a)Constructing a right angle and then bisecting it
- b)Measuring angles with a protractor
- c)Drawing a line segment, then creating an arc from one endpoint
- d)Using the Pythagorean theorem to find angles
Correct answer is option 'C'. Can you explain this answer?
What is the procedure for constructing a 60° angle using a ruler and compass?
a)
Constructing a right angle and then bisecting it
b)
Measuring angles with a protractor
c)
Drawing a line segment, then creating an arc from one endpoint
d)
Using the Pythagorean theorem to find angles
| | Trisha Vashisht answered |
To construct a 60° angle, you begin by drawing a line segment. Then, with one endpoint as the center, you draw an arc that intersects the segment. Using this intersection as the center and keeping the same radius, you draw another arc to intersect the first arc. Joining the first endpoint to this intersection point forms the desired 60° angle. This construction relies on the properties of equilateral triangles, where each angle measures 60°.
What is the first step in constructing a parallelogram when two consecutive sides and one diagonal are known?- a)Measuring the angles
- b)Constructing the sides
- c)Using a compass to find intersections
- d)Drawing the diagonal first
Correct answer is option 'D'. Can you explain this answer?
What is the first step in constructing a parallelogram when two consecutive sides and one diagonal are known?
a)
Measuring the angles
b)
Constructing the sides
c)
Using a compass to find intersections
d)
Drawing the diagonal first
| | EduRev Class 8 answered |
When constructing a parallelogram with two consecutive sides and one diagonal, the first step is to draw the diagonal. From one endpoint of this diagonal, you then draw arcs for the lengths of the consecutive sides to find the other vertices. This method emphasizes the geometric properties of parallelograms, particularly how the diagonals relate to the sides.
What is the method for constructing a rhombus when both diagonals are given?- a)Using a protractor to measure angles
- b)Finding the midpoints and constructing perpendicular bisectors
- c)Drawing the sides equal to the diagonals
- d)Connecting the vertices directly
Correct answer is option 'B'. Can you explain this answer?
What is the method for constructing a rhombus when both diagonals are given?
a)
Using a protractor to measure angles
b)
Finding the midpoints and constructing perpendicular bisectors
c)
Drawing the sides equal to the diagonals
d)
Connecting the vertices directly
| | Trisha Vashisht answered |
To construct a rhombus when both diagonals are given, you first draw one diagonal and find its midpoint by constructing the perpendicular bisector. From this midpoint, you then measure half the length of the other diagonal on both sides to determine the other vertices of the rhombus. Joining these points completes the rhombus. This method highlights how the properties of diagonals and symmetry are essential in constructing rhombuses.
How can you construct a line parallel to another line at a given distance?- a)Measuring the distance with a ruler
- b)Drawing a diagonal line
- c)Drawing a perpendicular line from the first line
- d)Using a compass to mark the distance
Correct answer is option 'C'. Can you explain this answer?
How can you construct a line parallel to another line at a given distance?
a)
Measuring the distance with a ruler
b)
Drawing a diagonal line
c)
Drawing a perpendicular line from the first line
d)
Using a compass to mark the distance
| | EduRev Class 8 answered |
To construct a line parallel to an existing line at a specified distance, you first draw a perpendicular line from a point on the original line. From this point, you then measure the desired distance along the perpendicular and mark a new point. Finally, you draw another line through this new point that is perpendicular to the first perpendicular line, creating a parallel line at the specified distance. This method illustrates the properties of parallel lines and how they can be constructed using perpendiculars.
What is the process to draw a perpendicular line from a point on a given line?- a)Measuring the angle with a protractor
- b)Drawing arcs from the point that intersect the line
- c)Using a compass to measure the distance from the point
- d)Extending the line to find a new angle
Correct answer is option 'B'. Can you explain this answer?
What is the process to draw a perpendicular line from a point on a given line?
a)
Measuring the angle with a protractor
b)
Drawing arcs from the point that intersect the line
c)
Using a compass to measure the distance from the point
d)
Extending the line to find a new angle
| | Trisha Vashisht answered |
To draw a perpendicular from a point on a line, you start by using the given point as the center to draw an arc that intersects the line at two points. From these points, you then draw arcs of equal radius which intersect at a point above or below the line. Joining the original point to this intersection point creates the perpendicular line. This construction emphasizes the geometric principles of perpendicularity without the need for physical angle measurement.
How do you construct a quadrilateral when four sides and one angle are given?- a)Drawing the sides in any order
- b)Using a diagonal to connect the sides
- c)Starting with the angles
- d)Constructing one side and then using arcs for the others
Correct answer is option 'D'. Can you explain this answer?
How do you construct a quadrilateral when four sides and one angle are given?
a)
Drawing the sides in any order
b)
Using a diagonal to connect the sides
c)
Starting with the angles
d)
Constructing one side and then using arcs for the others
| | EduRev Class 8 answered |
To construct a quadrilateral with four sides and one angle, you begin by drawing one side. At one endpoint, you construct the specified angle, marking the second side. Then, from the other endpoint of the second side, you draw arcs with the lengths of the remaining sides to find the intersection points, which complete the quadrilateral. This method emphasizes the relationship between sides and angles in quadrilateral constructions.
What is the process for constructing a 45° angle using a ruler and compass?- a)Drawing a 60° angle first
- b)Constructing a 90° angle and bisecting it
- c)Measuring angles with a ruler
- d)Using a protractor for accuracy
Correct answer is option 'B'. Can you explain this answer?
What is the process for constructing a 45° angle using a ruler and compass?
a)
Drawing a 60° angle first
b)
Constructing a 90° angle and bisecting it
c)
Measuring angles with a ruler
d)
Using a protractor for accuracy
| | EduRev Class 8 answered |
To construct a 45° angle, you first create a 90° angle using standard methods, such as drawing a line and using arcs. Once you have the 90° angle, you then bisect this angle to obtain the 45° angle. This technique is important because it illustrates how angles can be subdivided, showcasing the principles of angle bisection in geometry.
How can you construct the bisector of a given angle using a ruler and compass?- a)Reflecting the angle across a line
- b)Drawing an arc from the vertex and then constructing arcs from the intersection points
- c)By measuring the angle with a protractor and dividing it
- d)Drawing an equal angle on both sides of the original angle
Correct answer is option 'B'. Can you explain this answer?
How can you construct the bisector of a given angle using a ruler and compass?
a)
Reflecting the angle across a line
b)
Drawing an arc from the vertex and then constructing arcs from the intersection points
c)
By measuring the angle with a protractor and dividing it
d)
Drawing an equal angle on both sides of the original angle
| | EduRev Class 8 answered |
To bisect a given angle, you start by drawing an arc from the vertex that intersects both arms of the angle. Next, you take the intersection points and draw arcs of equal radius from each of them, which will intersect at a point inside the angle. Joining this point with the angle's vertex gives you the bisector, effectively dividing the angle into two equal parts. This method is foundational in geometric constructions and illustrates the concept of angle division.
What is the technique to construct a rhombus when one side and one angle are given?- a)Drawing all sides equal
- b)Constructing an angle and using arcs from the endpoints
- c)Drawing diagonals to find corners
- d)Using a square as a base
Correct answer is option 'B'. Can you explain this answer?
What is the technique to construct a rhombus when one side and one angle are given?
a)
Drawing all sides equal
b)
Constructing an angle and using arcs from the endpoints
c)
Drawing diagonals to find corners
d)
Using a square as a base
| | Trisha Vashisht answered |
To construct a rhombus given one side and one angle, you begin by drawing the specified side. From one endpoint, you construct the given angle to mark the next side. Then, using the same side length, you draw arcs from both endpoints to find the other two corners of the rhombus. This method highlights the properties of rhombuses, where all sides are equal in length.
When constructing a 30° angle, which angle is first created as part of the process?- a)15° angle
- b)45° angle
- c)90° angle
- d)60° angle
Correct answer is option 'D'. Can you explain this answer?
When constructing a 30° angle, which angle is first created as part of the process?
a)
15° angle
b)
45° angle
c)
90° angle
d)
60° angle
| | EduRev Class 8 answered |
To construct a 30° angle, you first create a 60° angle, as the 30° angle is half of 60°. After constructing the 60° angle using the described method, you then bisect it to achieve the desired 30° angle. This technique demonstrates the relationship between angles and the concept of angle bisectors, which is critical in geometric constructions.
Describe how to construct a parallelogram when two consecutive sides and the included angle are known.- a)Using the properties of triangles
- b)Drawing a rectangle first
- c)Drawing one side and using arcs for the second
- d)Measuring angles with a protractor
Correct answer is option 'C'. Can you explain this answer?
Describe how to construct a parallelogram when two consecutive sides and the included angle are known.
a)
Using the properties of triangles
b)
Drawing a rectangle first
c)
Drawing one side and using arcs for the second
d)
Measuring angles with a protractor
| | Trisha Vashisht answered |
To construct a parallelogram when two consecutive sides and the included angle are known, you start by drawing one side. From the endpoint of this side, you use the angle to draw the next side. After marking the length of the second side, you can then use arcs to find the necessary intersection points to complete the parallelogram. This construction relies on the fact that opposite sides of a parallelogram are equal in length and parallel.
How can you construct a square when two adjacent sides are given?- a)Drawing a line segment and constructing equal angles
- b)Creating a diagonal first
- c)Measuring angles with a protractor
- d)Drawing one side and using arcs to find the other
Correct answer is option 'D'. Can you explain this answer?
How can you construct a square when two adjacent sides are given?
a)
Drawing a line segment and constructing equal angles
b)
Creating a diagonal first
c)
Measuring angles with a protractor
d)
Drawing one side and using arcs to find the other
| | EduRev Class 8 answered |
To construct a square when given two adjacent sides, you first draw one side to the specified length. From one endpoint, you construct a 90° angle to establish the second side. After marking the length of the second side, you can then use arcs to find the remaining corners of the square. This construction demonstrates the importance of right angles and equal side lengths in defining squares.
Describe how to construct a perpendicular bisector of a line segment.- a)Drawing arcs from both endpoints of the segment with equal radius
- b)Extending the line segment to find the midpoint
- c)By measuring the length of the segment and dividing it in half
- d)Using a right angle at one endpoint
Correct answer is option 'A'. Can you explain this answer?
Describe how to construct a perpendicular bisector of a line segment.
a)
Drawing arcs from both endpoints of the segment with equal radius
b)
Extending the line segment to find the midpoint
c)
By measuring the length of the segment and dividing it in half
d)
Using a right angle at one endpoint
| | Trisha Vashisht answered |
To construct the perpendicular bisector of a line segment, you draw arcs from both endpoints of the segment using a radius greater than half the length of the segment. The arcs will intersect at two points. Joining these intersection points creates a line that bisects the segment at a right angle, effectively creating the perpendicular bisector. This method illustrates the concept of symmetry and the properties of bisectors in geometry.
What is the primary method used in constructing an angle equal to a given angle using a ruler and compass?- a)Drawing a line segment as the base and using arcs to find intersection points
- b)Measuring the angle with a protractor
- c)Drawing a right angle first
- d)Using a triangle to create the angle
Correct answer is option 'A'. Can you explain this answer?
What is the primary method used in constructing an angle equal to a given angle using a ruler and compass?
a)
Drawing a line segment as the base and using arcs to find intersection points
b)
Measuring the angle with a protractor
c)
Drawing a right angle first
d)
Using a triangle to create the angle
| | EduRev Class 8 answered |
To construct an angle equal to a given angle, you start by drawing a line segment as the base for the new angle. Then, using the vertex of the given angle as the center, you draw an arc that intersects both arms of the angle. By measuring the distance between the intersection points with a compass and replicating this distance from the vertex of the new angle, you can accurately create an angle equal to the original. This method emphasizes the use of geometric properties rather than physical measurements.
How do you create a line that is perpendicular to a given line from a point outside the line?- a)Drawing arcs from the given point to intersect the line
- b)Using a compass to find the midpoint
- c)Measuring the angle with a protractor
- d)Creating a right angle at the given point
Correct answer is option 'A'. Can you explain this answer?
How do you create a line that is perpendicular to a given line from a point outside the line?
a)
Drawing arcs from the given point to intersect the line
b)
Using a compass to find the midpoint
c)
Measuring the angle with a protractor
d)
Creating a right angle at the given point
| | EduRev Class 8 answered |
To create a perpendicular line from a point outside a given line, you begin by drawing arcs from the external point that intersect the line at two points. From these intersection points, you then draw arcs of equal radius that meet on the opposite side of the line. Joining the external point to this intersection creates the desired perpendicular line. This construction demonstrates the principles of perpendicularity and how to effectively use a compass and straightedge in geometric constructions.
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