Class 8 Maths Practical Geometry Special Quadrilaterals requiring less than 5 measurements

Special Quadrilaterals requiring less than 5 measurements

Earlier quadrilaterals required 5 measurements. Following special quadrilaterals require less than 5 measurements.

  • Square - 1 measurement required. When a side of the square is given, it is true that:
    • All sides of the square are equal.
    • All internal angles are right angles.

Hence, using SAS condition, the square can be drawn as:

 

Problem:Draw a square READ with RE = 5.1 cm.

 

Solution:

All sides of a square are equal and the interior angles are 90°.

Step1: Draw a line RE of 5.1 cm and an angle of 90° at point R and E.

Step2: As vertex A and D are 5.1 cm away from vertex E and R respectively, cut line segments EA and RD, each of 5.1 cm from these rays.

Step3: Join D to A.

 

Rhombus - 2 measurements required. When two diagonals side of the square is given, it is true that:

  • Diagonals of a rhombus are perpendicular bisectors of each other.

So if a diagonal of given length is drawn and another line is drawn as perpendicular bisector, of again given length, the rhombus can be formed.

 

 

Problem: Construct a RhombusBEND with following measurements.

BN = 5.6 cm, DE = 6.5 cm

 

Solution:

Step1: Draw Side BN = 5.6 cm and draw its perpendicular bisector. Let it intersect line segment BN at point O

Step2: Taking O as center, draw arcs of 3.25 cm radius to intersect the perpendicular bisector at point D and E

Step3: Join points D and E to points B and N

 

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