Geometry: An Interactive Journey to Mastery



Solutions

Lesson 8

1. i. b = c because vertical angles.
   ii. a = d because a = b, b = c, c = d from the givens and the previous step.
   iii. AB DE& because a and d are congruent alternate interior angles.


2. i. a + b EHFDXVHPSASR.
   ii. a + c EHFDXVHa and cDUHFRPSOHPHQWDU\ͼ௘5HFDOOWKHGH¿QLWLRQRI³FRPSOHPHQWDU\ ́IURP/HVVRQ
   ௘ͽ
   iii. baca   DQG  because of algebra.
   LY 6Rb = c.


3. i. Label the angles x 1 , x, y 1 , y, z, w as shown in
   Figure S.8.1.
   ii. x 1 # x because they are alternate interior angles
   for AB CD&.
   iii. y 1 # y because they are alternate interior angles
   for AD BC&.
   iv. wxyzxy   DQG    because
   WKHUHDUHƒLQDWULDQJOH
   v. w = z because x 1 = x and y 1 = y.
   That is, ‘#‘AC.
   &RPPHQW1RWLFHWKH¿UVWOLQH,WLVTXLWHDQLFHWHFKQLTXHWRODEHODQJOHVLQWKHGLDJUDPZLWKOHWWHUVDQG
   WKHQUHIHUWRWKRVHOHWWHUQDPHV,I\RXGRWKLVWKH¿UVWOLQHRI\RXUSURRIVKRXOGEH³L/DEHOWKHGLDJUDPDV
   VKRZQ ́

Aw

D z

B

C

x 1

x 2

y 2

y 1

Figure S.8.1