Geometry: An Interactive Journey to Mastery



4. i. Label the lengths a, b, x, y, z as shown in Figure S.8.2.
   ii. Triangles FUM and LUMDUHULJKWWULDQJOHVͼ௘ZLWKULJKWDQJOHDWU௘ͽ
   because UFAUM.
   iii. axyz    and byz  because RIWKH3\WKDJRUHDQ
   theorem.
   iv. a! b because x + y! y.
   That is, FM! LM.


5. i. Label angles a 1 , a, b, c, d, e as shown in Figure S.8.3.
   ii. a 1 = a because given.
   iii. e = a and d = a 1 because alternate interior angles for
   parallel lines.
   iv. d = a because of the previous two steps.
   v. d + c EHFDXVHUBAYB.
   vi. a + b EHFDXVHVDPHVLGHLQWHULRUDQJOHVDGGWRƒ
   vii. cdba   DQG   because of algebra.
   viii. b = c because a = d from step 4.
   That is, ‘#‘YUB RBU.


6. i. Label angle w as shown in Figure S.8.4.
   ii. z + w EHFDXVHRQDVWUDLJKWOLQH
   iii. x + y + w EHFDXVHƒLQDWULDQJOH
   iv. zwxyw    DQG  because of algebra.
   Y 6Rz = x + y.

F

U

L

M

a

b

x

y

z

Figure S.8.2

R

Y

U

B

a 1 a (^2) b
e d c
Figure S.8.3
x
y
w z
Figure S.8.4