help me drawing this maths problem?

Question

i don't know how to draw this and thats what i need help with. here is what the book asks:

ABCD is a parallelogram with angle BAD acute. E is on the ray (what is a ray?) CB such that triangle ABE is isosceles with AB=AE. F is on the ray CD such that triangle ADF is isosceles with AD = AF

and then it asks::

a. Prove that triangle ABE is similar to triangle ADF

b. Prove that DE = BF



ANOTHER QUESTION I HAVE TO DRAW AND SOLVE:

ABC is a triangle, M is a point in the line segment AB such that AB = 3AM and N is a point in the line segment AC such that AC = 3AN.

a. Prove that BC || MN

b. if BN and CM intersect at P, prove that BP = 3PN.

you don't have to help me with both, but if you can that would be great. all help i sgrealty appreciated

Answer 1

1. Something is wrong with your description. Recheck the statement.

2. In part a, you are creating a set of similar triangles ABC and AMN. Since they are similar, angle ABC is equal to angle AMN. This is sufficient to prove parallel lines (one of the parallel line theorms deals with a line drawn through both lines, and the angles).