Comp D From The Point B.) 2. 2080 Lalitpur Q.No. 10 Aax: 5:2 गर्नुहोस् 131 2. AB = 5 से.मि.. BC = 4 से.मि. र 4ABC = 60° भएको समानान्तर चतुर्भुज ABCD की रचना (Construct A Parallelogram ABCD In Which AB = 5 Cm, BC = 4 Cm And 4ABC = 60°.) B. दिएको चित्रमा

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Introduction

In this article, we will learn how to construct a parallelogram ABCD with given measurements. We will use the given information to draw the parallelogram and verify its properties.

Given Measurements

  • AB = 5 cm
  • BC = 4 cm
  • ∠ABC = 60°

Step 1: Draw a Line Segment AB

  • Start by drawing a line segment AB of length 5 cm.
  • This will be the base of our parallelogram.

Step 2: Draw an Arc with Center B and Radius 4 cm

  • Draw an arc with center B and radius 4 cm.
  • This arc will intersect the line segment AB at point C.

Step 3: Draw a Line Segment BC

  • Draw a line segment BC of length 4 cm.
  • This will be one of the sides of our parallelogram.

Step 4: Draw an Arc with Center C and Radius 5 cm

  • Draw an arc with center C and radius 5 cm.
  • This arc will intersect the line segment BC at point D.

Step 5: Draw a Line Segment CD

  • Draw a line segment CD of length 5 cm.
  • This will be the other side of our parallelogram.

Step 6: Draw a Line Segment DA

  • Draw a line segment DA of length 4 cm.
  • This will be the other side of our parallelogram.

Verification

  • Measure the length of the sides of the parallelogram.
  • Verify that the opposite sides are equal.
  • Verify that the adjacent angles are supplementary.

Conclusion

In this article, we learned how to construct a parallelogram ABCD with given measurements. We used the given information to draw the parallelogram and verified its properties. This construction can be used to verify the properties of a parallelogram and to solve problems involving parallelograms.

Properties of a Parallelogram

A parallelogram is a quadrilateral with opposite sides that are equal and parallel. The opposite angles of a parallelogram are also equal. The adjacent angles of a parallelogram are supplementary.

Importance of Constructing a Parallelogram

Constructing a parallelogram is an important skill in geometry. It can be used to verify the properties of a parallelogram and to solve problems involving parallelograms. It can also be used to construct other geometric shapes such as rectangles and squares.

Real-World Applications

Constructing a parallelogram has many real-world applications. It can be used in architecture to design buildings and bridges. It can also be used in engineering to design machines and mechanisms.

Conclusion

Q: What is a parallelogram?

A: A parallelogram is a quadrilateral with opposite sides that are equal and parallel. The opposite angles of a parallelogram are also equal. The adjacent angles of a parallelogram are supplementary.

Q: What are the properties of a parallelogram?

A: The properties of a parallelogram are:

  • Opposite sides are equal and parallel.
  • Opposite angles are equal.
  • Adjacent angles are supplementary.

Q: How do I construct a parallelogram?

A: To construct a parallelogram, you need to follow these steps:

  1. Draw a line segment AB of length 5 cm.
  2. Draw an arc with center B and radius 4 cm.
  3. Draw a line segment BC of length 4 cm.
  4. Draw an arc with center C and radius 5 cm.
  5. Draw a line segment CD of length 5 cm.
  6. Draw a line segment DA of length 4 cm.

Q: What are the advantages of constructing a parallelogram?

A: The advantages of constructing a parallelogram are:

  • It helps to verify the properties of a parallelogram.
  • It can be used to solve problems involving parallelograms.
  • It can be used to construct other geometric shapes such as rectangles and squares.

Q: What are the real-world applications of constructing a parallelogram?

A: The real-world applications of constructing a parallelogram are:

  • In architecture, it can be used to design buildings and bridges.
  • In engineering, it can be used to design machines and mechanisms.
  • In art, it can be used to create geometric patterns and designs.

Q: What are the common mistakes to avoid while constructing a parallelogram?

A: The common mistakes to avoid while constructing a parallelogram are:

  • Not drawing the line segments accurately.
  • Not drawing the arcs accurately.
  • Not verifying the properties of the parallelogram.

Q: How do I verify the properties of a parallelogram?

A: To verify the properties of a parallelogram, you need to:

  • Measure the length of the sides of the parallelogram.
  • Verify that the opposite sides are equal.
  • Verify that the opposite angles are equal.
  • Verify that the adjacent angles are supplementary.

Q: What are the benefits of learning how to construct a parallelogram?

A: The benefits of learning how to construct a parallelogram are:

  • It helps to improve your understanding of geometry.
  • It helps to improve your problem-solving skills.
  • It helps to improve your ability to visualize and create geometric shapes.

Q: How do I practice constructing a parallelogram?

A: To practice constructing a parallelogram, you can:

  • Draw multiple parallelograms with different measurements.
  • Verify the properties of each parallelogram.
  • Use different tools and techniques to construct the parallelogram.

Q: What are the resources available to learn how to construct a parallelogram?

A: The resources available to learn how to construct a parallelogram are:

  • Textbooks and online resources.
  • Video tutorials and online courses.
  • Practice problems and worksheets.