Question

Construct Rhombus MATH with AT = $4cm$ , $\angle MAT = {120^ \circ }$

Answer 1

Hint: First, draw the basic line segment, then draw the angle if required and take proper measurements on the ruler and using compass cut arcs and join them with precise measurements. Here the measurement of a segment and angle is given, so first, we will draw the segment and then the angle.

Complete step-by-step solution:
Rhombus is a parallelogram with all sides equal and opposite angles. The diagonals of a rhombus bisect each other and are equal.
Constructing steps:
Initially, draw a line segment $AT = 4cm$.

Next, construct the angle$\angle MAT = {120^ \circ }$.

With A as the centre and radius equal 4cm,
Draw an arc on $AX$
Mark the intersection as $M$

With $M$ as the centre and radius of $4cm$ horizontally. Draw an arc.
With $T$ as the centre with the same radius, cut the previous arc drawn with centre $M$ and mark the point as $H$.

Join points $MH$ and $HT$ .

∴ MATH is the required Rhombus.

Note: While drawing the arcs be careful about the measurements and draw arrows for segments drawn by an angle. Give proper naming and labels to each and every point, angle, length and segment.