Let ABC be an isosceles triangle at A. Let D be the midpoint of BC. On segment AD take any point E (E is different from A and D). Through E draw lines perpendicular to AB and AC at M, N, respectively. a) Prove that quadrilateral AMEN is a square.

b) Prove MN // BC.

c) Through M draw a line perpendicular to DN at F. Prove angle AFE = 90 degrees

d) Prove that B, E, F are collinear.

df =

both have same length

secant-secant formula:

(whole secant) x (external part) =           (whole secant) x (external part)

(8+y-2) *8=                                           (y+4+6) *6

(y+6)*8 = (y+10) *6

distribute

8y+48 = 6y +60

subtract 6y from each side

2y +48 = 60

subtract 48 from each side

2y = 12

divide by 2

y = 6

sv =     (y+4+6)

sv   = 6+4+6

sv = 16