Q. 1

# 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}.

Answer :

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.

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