Answer:
a) 
b) 
Step-by-step explanation:
Q11 a) ABCD is a parallelogram, then  units.
 units.
Consider triangles AED and BEF. In these triangles 
 by reflexive property;
 by reflexive property;
 are corresponding angles formed when parallel lines BC and AD are intersected by transversal AE. By corresponding angles theorem, they are congruent.
 are corresponding angles formed when parallel lines BC and AD are intersected by transversal AE. By corresponding angles theorem, they are congruent.
By AA similarity theorem,  . Similar triangles have proportional corresponding parts, so
. Similar triangles have proportional corresponding parts, so
![\dfrac{AE}{BE}=\dfrac{AD}{BF}\\ \\\dfrac{12+6}{6}=\dfrac{8}{x}\\ \\18x=48\ [\text{Cross multoply}]\\ \\x=\dfrac{48}{18}=\dfrac{8}{3}=2\dfrac{2}{3}\ units](https://tex.z-dn.net/?f=%5Cdfrac%7BAE%7D%7BBE%7D%3D%5Cdfrac%7BAD%7D%7BBF%7D%5C%5C%20%5C%5C%5Cdfrac%7B12%2B6%7D%7B6%7D%3D%5Cdfrac%7B8%7D%7Bx%7D%5C%5C%20%5C%5C18x%3D48%5C%20%5B%5Ctext%7BCross%20multoply%7D%5D%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B48%7D%7B18%7D%3D%5Cdfrac%7B8%7D%7B3%7D%3D2%5Cdfrac%7B2%7D%7B3%7D%5C%20units)
ABCD is a parallelogram, then  units, so
 units, so

Q11b) ABCD is a parallelogram, then  units. By segment addition postulate,
 units. By segment addition postulate,

Consider triangles EBF and ECD. In these triangles, 
 by reflexive property
 by reflexive property
 are corresponding angles formed when parallel lines AB and CD are intersected by transversal EC. By corresponding angles theorem, they are congruent.
 are corresponding angles formed when parallel lines AB and CD are intersected by transversal EC. By corresponding angles theorem, they are congruent.
So,  by AA similarity theorem. Similar triangles have proportional corresponding parts, so
 by AA similarity theorem. Similar triangles have proportional corresponding parts, so

From the first equality,

From the second equality:
