Question 942045
{{{drawing(800,250,-4,4,-0.3,2.2,
triangle(-3,0,-2,0,-2,1.732),
triangle(3,0,2,0,2,1.732),
rectangle(2,0,2.1,0.1),rectangle(-2,0,-2.1,0.1),
line(-4,0,4,0),line(-2,1.732,2,1.732),
locate(-3.04,0,T),locate(-2.04,0,P),
locate(-2.04,1.95,Q),locate(1.96,1.95,R),
locate(2.96,0,S),locate(1.96,0,O),
locate(-2.5,0.9,2cm),locate(2.57,0.9,2cm)
red(arc(-3,0,0.8,0.8,-60,0)),locate(-2.9,0.25,red(60^o)),
red(arc(3,0,0.8,0.8,180,240)),locate(2.65,0.25,red(60^o))
)}}} Triangles TPQ and ROS are congruent by Angle-Angle-Side, because they have
congruent pairs of {{{90^o}}} Angles, followed by
congruent pairs of {{{60^o}}} Angles, and then
congruent pairs of {{{2cm}}} Sides.
Since triangles QPT and ROS are congruent, their corresponding parts,
including sides QP and RO, are congruent.
The lengths of RO, and QP are the same and are the distance between parallel lines QR and TS.
QRST is an isosceles trapezoid.
 
NOTE:
For your drawing,
QROP is a rectangle.
The lengths, in cm, are
{{{RO=QP=2*sin(60^o)=2*(sqrt(3)/2)=sqrt(3)=1.732}}} ,
{{{TP=SO=2*cos(60^o)=2*(1/2)=1}}} , and
{{{QR=OP=4cm}}} .