Construct a trapezium ABCD with AB||CD where AB=6cm, CD=4cm, /_A= 70°, /_ABD =30°.

Question

Construct a Trapezium from the chapter construction of quadrilaterals page number 214 of CBSE book..... class 8

Answer 1

Conventionally, the word CONSTRUCT (v) means to use only straightedge and compass.

 

You can construct the 30 degree angle, and you can choose any line segment length CD, calling it 4 units, and therefore you would also be able to construct segment AB of length 6 (using a copy of the 4 added to the bisection of the "4").

 

Therefore you can make a Z shape beginning with AB=6 at top of page, and a 30⁰ angle at B, and from there, runnng downward some distance to point D, then construct DC=4 being parallel to AB due to also constructing angle BDC = 30^o. BUT...

 

The problem is, however, there's no strict construction for the 70^o angle at A, beneath AB, which will enable a ray from A to be drawn so that intersects the diagonal emanating from B down to find point D.

 

It seems that the 70 degree angle at A would have to be made using a protractor--and that (to me, a traditionalist), is not allowed in the strict, classical Euclidean construction sense. But using the contractor would enable you to DRAW the desired trapezium (which was only called a trapezoid in my day).

Answer 2

By definition, a "trapezium" has no parallel sides, so you must be talking about a trapezoid (which has one pair of parallel sides). Also, your trapezoid appears to be misnamed: we must draw it as ABDC in order to have an angle ABD.

First, draw side AB with length of 6cm, and then draw CD with length 4cm, such that angle BAC is 70-degrees and angle ABD is 30-degrees. Since AB and CD are parallel, angles BAC and ACD are supplementary, so angle ACD is 110-degrees. This leaves angle CDB with 360 - (30+70+110) = 150-degrees.

Now form a right triangle with hypotenuse AC by drawing a line perpendicular to AB which intersects CD at point C. This new triangle will have angle measurements of 90-, 70, and 20-degrees. Draw a second right triangle with hypotenuse BD by drawing a line perpendicular to AB and intersecting point D (forming a right triangle with angles of 90-, 30-, and 60-degrees).

If you slide these two right triangles together, the base will measure 2cm (6cm – 4cm) and the opposite angle will measure 80-degrees (20-degrees plus 60-degrees). By the Law of Sines, you will get AC = 1.0154cm and BD = 1.908cm.