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Constructing a Quadrilateral

Constructing a Quadrilateral. When four sides and one diagonal are given. When two diagonals and three sides are given. When two adjacent sides and three angles are given. When three sides and two included angles are given. When other special properties are known.

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Constructing a Quadrilateral

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  1. Constructing a Quadrilateral

  2. When four sides and one diagonal are given. When two diagonals and three sides are given. When two adjacent sides and three angles are given. When three sides and two included angles are given. When other special properties are known. We shall learn how to construct a unique quadrilateral by following methods :-

  3. Example : Construct a quadrilateral PQRS where PQ = 4cm, QR = 6cm, RS= 5cm, PS = 5.5cm and PR = 7cm Constructing a quadrilateral when four sides and one diagonal are given Q 6 cm 4 cm P R 7 cm 5 cm 5.5 cm S ROUGH SKETCH

  4. Step 1 :-Construct a triangle PQR using SSS criterion. Q 6 cm 4 cm R P 7 cm

  5. Step 2 :-With P as centre draw an arc of radius 5.5 cm . Q 6 cm 4 cm R P 7 cm

  6. Step 3 :-Now, with R as centre draw an arc of radius 5 cm intersecting another arc at point S Q 6 cm 4 cm R P 7 cm S

  7. PQRS is the required quadrilateral. Step 4 :-Now join PS and RS. Q 6 cm 4 cm P R 7 cm S

  8. Example : Construct a quadrilateral ABCD, given that BC =4.5 cm, AD = 5.5 cm, CD = 5 cm, AC = 5.5 cm and diagonal BD = 7 cm. Constructing a quadrilateral when two diagonals and three sides are given. C 5 cm 4.5 cm 7 cm B D 5.5cm 5.5 cm A ROUGH SKETCH

  9. Step 1 :-Draw triangle ACD using SSS criterion D 5.5 cm 5 cm A C 5.5 cm

  10. Step 2 :-With D as centre draw an arc of radius 7 cm. D 5.5 cm 5 cm A C 5.5 cm

  11. Step 3 :-Now, with C as centre draw an arc of radius 4.5 cm intersecting another arc at point B. D 5.5 cm 5 cm A C 5.5 cm B

  12. Step 4 :-Join AB, DB and CB D 5.5 cm 5 cm 7 cm A C 5.5 cm ABCD is required triangle 4 cm B

  13. Constructing a Quadrilateral when two adjacent sides and three angles are known M 6.5 cm T I 3.5 cm ROUGH SKETCH S

  14. X I M 3.5 cm

  15. Y X S 6.5 cm I M 3.5 cm

  16. Z Y X S I M 3.5 cm

  17. Step 4 :-Mark that point T where SY and MZ meet. Z MIST is the required Quadrilateral. Y T X S I M 3.5 cm

  18. Constructing a quadrilateral when three sides and two included diagonals are given. 6.5 cm D C 5 cm B A 4 cm ROUGH SKETCH

  19. X C B 5 cm

  20. X A 4 cm C B 5 cm

  21. Y X 4 cm C B 5 cm

  22. Y D X 6.5 cm 4 cm C B 5 cm

  23. Y X D ABCD is the required Quadrilateral. 6.5 cm 4 cm C B 5 cm

  24. Some examples are :- • Draw a square of side 5 cm. • Construct a rhombus ABCD where AC = 6 cm, and BD = 7 cm. Constructing a Quadrilateral when other special properties are known.

  25. Example 1 :-Draw an square ABCD of side 5 cm. Initially it appears that only one measurements has been given. Actually we have many more details with us, because the figure is special quadrilateral namely a square. We know that each of its angles is a Right angle. 4.5 cm C D 4.5 cm 4.5 cm B A 4.5 cm

  26. As we know the diagonals of Rhombus are Perpendicular bisectors of one another. So, first we draw AC = 7 cm and construct its perpendicular bisector. Let them meet at O. cut off 3 cm lengths on either side of the drawn bisector . You get now B and D. Example 2 :-Construct a rhombus ABCD where AC = 6 cm, and BD = 7 cm. D 6 cm A O C 7 cm B

  27. The END

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