Geometry: An Interactive Journey to Mastery



YLL 6Rx y because x 1 = x and y 1 = y.

viii. x = y because of algebra.

ix. x 3 = x because of vertical angles.

x. y = x 3 because of the previous two steps.

xi. FL GK& because x 3 and y are congruent alternate interior angles.

10. 3URYH$QJOHVx and yKDYHWKHVDPHPHDVXUH௘6HHFigure S.8.8௘
    Proof
    i. Label another angle z, as shown in Figure S.8.9.
    ii. xz ƒ DQGyz ƒ because each form a straight angle.
    LLL 6Rx + z = y + z, giving x = y.

Lesson 9

1. D௘ͽ ++HYB~ LYKEHFDXVHRI$$ͼ௘VKDUHYHUWLFDODQJOHVDQG‘#‘BK௘ͽ
   E௘ͽ k 14 .
   F௘ͽ x ƒ
   G௘ a 814  gives a  7.


2. D௘ͽ 7KHWULDQJOHVDUHaEHFDXVHRIWKH$$SULQFLSOHͼ௘7KH\VKDUHWKHDQJOHDWWKHWRSDQGKDYHDQJOHVRIƒ
   LQFRPPRQ௘ͽ
   E௘ͽDQGF௘ͽ small big
   xyb
   yxa
   wf

l

l

l

G௘ͽ :HKDYHyb xa fxw y.

xy

Figure S.8.8

Figure S.8.9

xyz