Hints:

For #8 on pg 71. I did it by :

• extending side BA beyond A, and I used the exterior angle as one of the angles I used.
• constructing a point A' on BC such that BA'=BA, and considering the triangle A'BD.
• Somewhere along the way, I used all of these angles:
  • exterior angle at A
  • interior angle at A (DAB)
  • the two congruent angles at B (ABD and CBD)
  • the angles on either side of A' (BA'D and CA'D)
  • the angle at C (DCA')

For I.21, I recommend first proving this lemma: Given triangle ABC and point D on side BC, then the sum of AD and DC is shorter than the sum of AB and BC and angle ADC is greater than angle ABC.