Geometry: An Interactive Journey to Mastery

Solutions

8. &RQVLGHUDWULDQJOHZLWKVLGHOHQJWKVa, b, and c, as shown in
   Figure S.5.8.
   a + b + c = perimeter
   ,Ic is longer than half the perimeter, then a + b is less than half
   the perimeter. This means that a + b is smaller than c. But this is
   impossible. For a triangle, we need a + b!c.


9. ,IWKHWKUHHSRLQWVA, B, and C are not collinear, then they
   IRUPDWULDQJOH௘6HHFigure S.5.9௘
   %\WKHWULDQJXODULQHTXDOLW\WKHWKUHHGLVWDQFHVVDWLVI\
   AB + BC!AC.
   But we are told that AB + BC = AC. This means that the points
   cannot form a triangle and, therefore, must be collinear.
   10.Label the lengths x and d, as shown in
   Figure S.5.10.
   %\WKH3\WKDJRUHDQWKHRUHPx = a + b.
   %\WKH3\WKDJRUHDQWKHRUHPIRUWKHVKDGHG
   triangle, d = x + c = a + b + c.
   6RPQd abc  .
   Lesson 6


10. D௘ͽ 117.
    E௘ͽ 18.
    F௘ͽ 
    G௘ͽ 
    H௘ͽ 

a

b

c

Figure S.5.8

A

B

C

Figure S.5.9

c

a

P b

Q

x

d

Figure S.5.10