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Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral?
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Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and ang...
Constructing Quadrilateral ABCD
To construct quadrilateral ABCD with the given dimensions and angles, follow these steps:
1. Draw Side AB
- Start by drawing a line segment AB of length 10 cm.
2. Construct Angle A
- At point A, use a protractor to measure and draw an angle of 65°.
3. Draw Side AD
- From point A, measure 12 cm along the direction of the angle to mark point D.
4. Draw Side BC
- At point B, construct a line parallel to AD. Measure 12 cm along this line to find point C.
5. Complete the Quadrilateral
- Connect points D and C to complete quadrilateral ABCD.
Characterizing Quadrilateral ABCD
- Opposite Sides Equal: The quadrilateral has two pairs of opposite sides that are equal:
- AB = CD = 10 cm
- AD = BC = 12 cm
- Angle Properties: The angle A measures 65°.
- Special Name:
- This quadrilateral is classified as a Cyclic Quadrilateral because the sum of opposite angles is supplementary (Angle A + Angle C = 180°).
Conclusion
In summary, quadrilateral ABCD exhibits properties of both a parallelogram and a cyclic quadrilateral due to its equal opposite sides and the presence of an angle. This construction demonstrates the unique characteristics of cyclic quadrilaterals, making it an interesting geometric figure in Euclidean space.
To construct quadrilateral ABCD with the given dimensions and angles, follow these steps:
1. Draw Side AB
- Start by drawing a line segment AB of length 10 cm.
2. Construct Angle A
- At point A, use a protractor to measure and draw an angle of 65°.
3. Draw Side AD
- From point A, measure 12 cm along the direction of the angle to mark point D.
4. Draw Side BC
- At point B, construct a line parallel to AD. Measure 12 cm along this line to find point C.
5. Complete the Quadrilateral
- Connect points D and C to complete quadrilateral ABCD.
Characterizing Quadrilateral ABCD
- Opposite Sides Equal: The quadrilateral has two pairs of opposite sides that are equal:
- AB = CD = 10 cm
- AD = BC = 12 cm
- Angle Properties: The angle A measures 65°.
- Special Name:
- This quadrilateral is classified as a Cyclic Quadrilateral because the sum of opposite angles is supplementary (Angle A + Angle C = 180°).
Conclusion
In summary, quadrilateral ABCD exhibits properties of both a parallelogram and a cyclic quadrilateral due to its equal opposite sides and the presence of an angle. This construction demonstrates the unique characteristics of cyclic quadrilaterals, making it an interesting geometric figure in Euclidean space.
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Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral?
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Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral?.
Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Construct a quadrilateral ABCD in which AB=CD=10cm, AD=BC=12cm and angle A= 65°. What special name can you give to this quadrilateral?.
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