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JAWAHAR NAVODAYA VIDYALAYA, MAU U.P.�CLASS-VIII�Mathematics

PRACTICAL GEOMETRY

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Introduction

  • We have learnt how to draw triangles in earlier classes for this we required three measurement to draw a unique triangle. Since three measurement were enough to draw a triangle. Now a natural question arises whether four measurement would be sufficient to draw a unique four sided closed figure namely a quadrilateral. We have to focus only the construction of quadrilateral like figure.

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Constructing a quadrilateral

  • We shall learn how to construct a unique quadrilateral given the following measurements
  • (i) When four sides and one diagonal are given
  • (ii) When three sides and two diagonals are given
  • (iii) When two adjacent sides and three angles are given.
  • (iv) When three sides and two included angles are given.
  • (v) When other special properties are given.
  • Let us now we discuss these constructions one-by-one.

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When the lengths of four sides and a diagonal are given

  • With the help of a above information the quadrilateral can be constructed by taking an example of definite measurements as:

Construct a quadrilateral PQRS here PQ=4cm, QR=6cm, RS=5cm, PS=5.5cm and PR=7cm.

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Construction:

  1. First we draw a line segment PR of 7cm. From point P & R make two arcs of measurement 4cm and 6 cm joining a point Q as PQ and PR.
  2. Again from point P & R making two another arcs of measurement 5.5cm and 5cm as intersecting point S.
  3. Join PS & RS.
  4. This is the final construction of Quadrilateral PQRS.

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When three sides and two diagonals are given:

  • Construct a quadrilateral ABCD, given that BC=4.5cm, AB=5.5cm, CD=5cm and diagonals AC=5.5cm and BD=7cm.
  • Construction:

(i)First we draw a diagonal AC=5.5cm.

(ii) from points A & C draw two arcs cut at point D. Joint AD & CD.

(iii) Again draw two arcs from point A & C of definite measurements cuts at point B. Joint AB & CD.

This is final quadrilateral ABCD.

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When three angles and two adjacent sides are given:

  • Construct a Quadrilateral MIST where MI=3.5cm, IS=6.5cm, angle M=750,angle I= 1050 angle S= 1200
  • Construction: (i) To construct a quadrilateral MIST, first we draw a line segment MI=3.5cm

(ii) From point I make a angle 1050 and draw a line IX.

(iii) From line IX cut 6.5cm IS.

(iv) From point S draw a line SY making angle 1200 .

(v) Again from point M draw line segment MZ making angle 750 . SY and MZ cut at point T.

This is the final quadrilateral MIST.

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When three sides and two included angles are given:

  • To construct a quadrilateral ABCD where AB=4cm, BC=5cm, CD=6.5cm and angle B= 1050 and angle C= 800
  • Construction:(i) Start with taking BC=5cm on B

(ii) Draw an angle of 1050 along BX. Locate a point A =4cm away from this. Now we three point B,C,A.

(iii) The fourth point D is on CY which is inclined at 800 on BC

(iv) D is at a distance of 6.5cm on CY with C as center draw an arc of length 6.5cm. It cuts CY at D.

(v) Complete a quadrilateral ABCD.

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A Rhombus

  • Draw a Rhombus whose diagonals AC &DB are 7cm & 6cm resp.
  • Construction:

(i) For the construction of a rhombus we have

to draw two diagonals AC & DB of definite measurement intersecting at right angle to each other.

(ii) Now join AB,BC,CD & DA

(III) This is the complete rhombus ABCD.

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