Construct quadrilaterals with the measurements given below:

Quadrilateral HELP with HE = 6cm, EL = 4.5 cm, ∠H=60^o, ∠E =105^o and ∠P= 120^o.

GIVEN : In Quadrilateral HELP,

HE = 6cm

EL = 4.5 cm

∠H=60^o

∠E =105^o

∠P= 120^o

PROCEDURE :

Step 1: draw a rough sketch of the Quadrilateral HELP and mark the given measurements.

As we can see that ∠P is not between the given 2 sides , so we now find the ∠L that is between HE and EL using the property of sum of all angles of a quadrilateral ie. ∠L = 360° - (∠H + ∠E + ∠P) = 360° - (60° + 105° + 120°) = 75°.

∴ ∠L = 75°.

Step 2: construct ΔHEL using SAS property of construction model with HE = 6cm , ∠E = 105^o and EL = 4.5 cm.

Step 3 : Construct ∠H = 60° and draw HY .

( how to draw 60° angle ?

⇒ an arc is drawn from H . let it intersect HE at H’ . with center H’ and with same radius draw 2 arcs to cut at 2 points A,B which gives 60° and 120° respectively.

So , draw a line from H which passes through A to get the required angle. )

Step 4 : construct ∠L = 75^o and draw LZ to meet HY at P.

HELP is the required quadrilateral.