Draw a line l. Draw a perpendicular to I at any point on l on this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to I.
Let I be a line and P be a point not on I. Through P, draw a line m parallel to l. Now join P to any point Q on l. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet I at S. What shape do the two sets of parallel lines enclose?
Construct \[\Delta PQR\] if \[PQ=5cm,\] \[m\angle PQR={{105}^{\text{o}}}\]and \[m\angle QRP={{40}^{\text{o}}}\](Hint: Recall angle-sum property of a triangle).
Examine whether you can construct \[\Delta \text{DEF}\] such that \[\text{EF}=\text{7}.\text{2 cm},\text{ m }\angle E=\text{11}{{0}^{\text{o}}}\] and \[m\angle F={{80}^{\text{o}}}\]. Justify your answer.