Geometry: An Interactive Journey to Mastery



:HKDYHWKHIROORZLQJ

x = 60

R

S^2 x = 120

Figure S.7.6

6DPHVLGHLQWHULRUDQJOHVVXPPLQJWRƒJLYHVST RQ&.

7. D௘ͽ %HFDXVH ZHKDYHVDPHVLGHLQWHULRUDQJOHVDGGLQJWRƒ7KLVPHDQVWKDWGB LO&.
   E௘ͽ 1Rz


8. D௘ͽ z # r gives congruent alternate interior angles, making OU TS&.
   E௘ͽ y # qGRHVQ¶WLPSO\DQ\WKLQJ
   F௘ͽ yͼ௘x + r௘ͽ JLYHVVDPHVLGHLQWHULRUDQJOHVDGGLQJWRƒ\LHOGLQJOU TS&.


9. %HFDXVHWKHUHDUHƒLQDSHQWDJRQ
        
   ƒ

yyy

y

y



Looking at same-side interior angles, x 

giving x ƒ

Finally, z + y JLYHVz ƒ

10. i. ... because they are vertical angles.
    iii. ... because a and e are congruent alternate interior angles.

3 y

y^2 y

x

z

(^55160)
105
20 140
Figure S.7.7