In give figur `l abs() m` and M is the mid-point of a line segment AB .Show that M is also the mid- point of any line segment CD,having its end points on l and m,respectively.

Explanation

Given in the figure,` l abs()` m and mid -Point of a line segment AB i.e AM =BM
`Proof brecause " "l abs () m " [given ]`
`" "angleBAC=angleABD " " ["altermate interior angles" ]`
`" "angleAMC = angleBMD " " ["vertically opposite angles" ]`
`In Delta AMC and Delta BMD " " angleBAC=angleABD " " ["Proved above "]`
`AM=BM " "["given"]`
`and " " angleAMC =angleBMD " "["proved above "]`
`because " " Delta AMC cong Delta BMD " ["by ASA congruence rule"]`
`rArr " MC=MD " " [" by CPCT "]`