ROUTERA

Chapter 11 Constructions

Class 10th Maths Chapter Case Study Questions

Case Study 1: Constructing a Triangle

Case Description:
An architect is designing a triangular garden. She has the lengths of two sides and the included angle between them. The two sides measure 7 cm and 5 cm, and the included angle is 60°. To accurately visualize the garden layout, she needs to construct the triangle using a compass and straightedge.

The architect will use the construction steps for a triangle given two sides and the included angle:

  1. Draw a line segment measuring 7 cm.
  2. At one endpoint, use a protractor to measure and draw a 60° angle.
  3. From this angle, mark a 5 cm arc, intersecting with the 7 cm line.
  4. Connect the intersection points to complete the triangle.

MCQs:

  1. What is the length of the first side of the triangle?

    • A) 5 cm
    • B) 7 cm
    • C) 10 cm
    • D) 12 cm

  2. What angle is used in the construction?

    • A) 45°
    • B) 60°
    • C) 75°
    • D) 90°

  3. What is the purpose of using a compass in this construction?

    • A) To measure angles
    • B) To measure distances
    • C) To draw arcs
    • D) To create straight lines

  4. Which step involves the use of a protractor?

    • A) Drawing the line segment
    • B) Measuring the angle
    • C) Marking the arc
    • D) Connecting the intersection points

Case Study 2: Constructing a Bisector

Case Description:
A geometry teacher wants to illustrate the concept of angle bisectors in her class. She decides to construct the bisector of a 70° angle to show how it divides the angle into two equal parts. Using a protractor and compass, she follows the construction steps.

The steps include:

  1. Drawing an angle of 70° using a protractor.
  2. Placing the compass point on the vertex and drawing an arc that intersects both rays of the angle.
  3. Labeling the points where the arc intersects the rays as A and B.
  4. Keeping the compass width as the distance between A and B and drawing arcs above the angle.
  5. Drawing a straight line from the vertex through the intersection of the arcs to form the bisector.

MCQs:

  1. What is the measure of the angle to be bisected?

    • A) 60°
    • B) 70°
    • C) 80°
    • D) 90°

  2. What is the purpose of the arcs drawn after marking points A and B?

    • A) To measure the angle
    • B) To create the bisector
    • C) To find the intersection
    • D) To extend the angle

  3. How many equal angles will the angle bisector create?

    • A) 1
    • B) 2
    • C) 3
    • D) 4

  4. What tool is used to ensure the arcs are drawn accurately?

    • A) Ruler
    • B) Protractor
    • C) Compass
    • D) Set square

Case Study 3: Constructing a Square

Case Description:
A landscape designer plans to create a square garden. To accurately construct the garden, she starts by marking one side of the square, measuring 4 m. The designer will then use a compass and straightedge to ensure the other sides are equal and form a right angle.

The steps include:

  1. Drawing the first side of the square, measuring 4 m.
  2. Using the compass to mark the end of the side, drawing an arc of 4 m to find the position of the adjacent side.
  3. Drawing perpendicular lines at both endpoints using a set square or a compass.
  4. Marking the final point to complete the square and checking the dimensions to ensure all sides are equal.

MCQs:

  1. What is the length of each side of the square?

    • A) 2 m
    • B) 3 m
    • C) 4 m
    • D) 5 m

  2. Which tool is primarily used to ensure the angles are right angles?

    • A) Ruler
    • B) Protractor
    • C) Set square
    • D) Compass

  3. How many sides does a square have?

    • A) 3
    • B) 4
    • C) 5
    • D) 6

  4. What is the total perimeter of the square garden?

    • A) 12 m
    • B) 16 m
    • C) 20 m
    • D) 24 m

Case Study 4: Constructing a Tangent

Case Description:
A student is learning about tangents to circles and wants to construct a tangent line from a point outside a circle to the circle. The circle has a radius of 5 cm, and the external point is 8 cm away from the center of the circle.

The student follows these construction steps:

  1. Draw the circle with a radius of 5 cm.
  2. Mark the center and label it O.
  3. From point P (8 cm from O), draw a line segment to O.
  4. Use a compass to find the midpoint of line OP and draw a circle with the midpoint as the center and radius equal to half of OP.
  5. The points where the circle intersects the original circle will determine the points from which to draw the tangents.

MCQs:

  1. What is the radius of the circle?

    • A) 4 cm
    • B) 5 cm
    • C) 6 cm
    • D) 7 cm

  2. What is the distance from the external point P to the center O?

    • A) 5 cm
    • B) 6 cm
    • C) 7 cm
    • D) 8 cm

  3. What is the purpose of finding the midpoint of OP?

    • A) To measure the angle
    • B) To create the tangents
    • C) To draw the circle
    • D) To bisect the line

  4. How many tangents can be drawn from an external point to a circle?

    • A) 1
    • B) 2
    • C) 3
    • D) 4

Case Study 5: Constructing Parallel Lines

Case Description:
An artist wants to create a pattern with parallel lines for a mural. To ensure the lines are perfectly parallel, the artist will use a straightedge and a compass to construct two parallel lines spaced 3 cm apart.

The steps include:

  1. Draw a straight line using the straightedge.
  2. Choose a point above or below the line where the parallel line will be located.
  3. Using the compass, set the width to 3 cm and draw arcs from the two ends of the original line.
  4. Connect the intersection points of the arcs to form the parallel line.

MCQs:

  1. How far apart are the two parallel lines?

    • A) 2 cm
    • B) 3 cm
    • C) 4 cm
    • D) 5 cm

  2. Which tool is primarily used to ensure the lines are straight?

    • A) Protractor
    • B) Ruler
    • C) Compass
    • D) Set square

  3. What type of lines is the artist constructing?

    • A) Perpendicular
    • B) Intersecting
    • C) Parallel
    • D) Curved

  4. Why is it important to use a compass in this construction?

    • A) To measure angles
    • B) To ensure uniform spacing
    • C) To draw arcs
    • D) To create straight lines