Question

Construct $△$DEF such that DF = 6.2 cm , $\angle$DEF = 60$°$ ,EM$\perp$DF and EM = 4.4 cm.

Answer 1

Steps of Construction:-
(i) Draw a line segment DF = 6.2 cm.
(ii) Through D draw DY such that $\angle$FDY= 60$°$
(iii) Draw DX$\perp$DY
(iv) Draw the perpendicular bisector of DF intersecting DX at O and DF at H.
(v) With O as centre and OD as radius, draw the circle
(vi) The major arc DWF of the circle,contains the vertical 60$°$
(vii) With H as centre cut off HP = 4.4 cm
(viii) Draw a line EE' parallel to DF passing through P.
(ix)With E as centre draw a line parallel to PH intersecting DF at M.
(x) Join ED and EF.

$△$DEF or $△$DE'F is the required triangle.