Q. 44.2( 37 Votes )

# Construct the quadrilaterals with the given measurements. And write steps of construction.

Rhombus MATH with AT = 4 cm, ∠MAT = 120^{o}.

Answer :

GIVEN : In Rhombus MATH,

AT = 4 cm

∠MAT = 120^{o}

PROCEDURE :

Step 1 : Draw a rough sketch of the required quadrilateral and mark the given measurements.

Here , we are given only 2 measurements. But as MATH is a rhombus , we can also write that MA = AT = TH = HM = 4cm.

(now we got 5 measurements in total)

Step 2 : Draw ΔMAT using S.A.S property of construction , by taking MA = 4 cm , ∠ MAT = 120° and AT = 4 cm.

Step 3 : To locate the fourth vertex ‘H’ , draw an arc , with center T and radius 4cm (TH=4cm).

Draw another arc with center M and radius 4 cm (MH=4cm) which cuts the previous arc at H.

Step 4: Join TH and MH to complete the required rhombus MATH.

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