Geometry
REVIEW: Chapter 3 KEY
1. plane SVX
2. possible answers: VZ , XS , VU , ST
3. Alternate Exterior s Theorem
4. Alternate Interior s Theorem
5. Corresponding s Postulate
6. m13 = 94 (Consecutive Interior s are supplementary. 180 – 86 = 94)
7. x = 13
(Set up and solve 6x – 5 = 5x + 8 since Alternate Interior s are )
y = 39
(Plug x into 10 (so m10 = 73). 9 and 10 are supplementary. Set up and solve: 73 + 3y – 10 = 180)
5  4
3
8. m =
(Simplify
)
5  10
5
9. 397 memberships
(2007: 173 memberships; 56 memberships per year for 4 years is 224 memberships. 173 + 224 = 397)
6  9
4  12
10. Neither
(Simplify
and
. The slopes are not the same. The slopes are not opposite reciprocals.)
6 1
5 1
4  10
26
11. Parallel
(Simplify
and
. The slopes are the same.)
3  5
1  2
12. a) C = 1.18p + 12
b) $71
(plug 50 in for p in the equation from part a)
13. y = –9x + 3
14. y = 3x + 8
(Set up and simplify: y – 5 = 3(x + 1))
1
15. y  x  1
3
1  0
(Determine the 2 given ordered pairs: (3, 0) is on the x-axis at 3; (0, –1) is on the y-axis at –1. Simplify
to find the slope. Use
03
the slope and the given y-intercept to write the equation of the line.)
1
16. y   x  17
3
(Perpendicular lines have opposite reciprocal slopes, so take the opposite reciprocal of the given slope, 3. Plug the slope and the given
1
point into point-slope form and simplify: y  16   ( x  3) )
3
17. AB || DE by Alternate Interior s Converse
18. AD || BE by Corresponding s Converse
19. AD || BE by Consecutive Interior s Converse
20. a) x = 18
(Set up and solve: 9x – 44 = 6x + 10, since Alternate Exterior s are )
20. b) x = 43
(Set up and solve: 7x – 2 + 10 – 3x = 180, since Consecutive Interior s are supplementary)
21.
22. The distance between (3, 3) and x = –5 is 8.
(Count the units it takes to get from the point to the vertical line)
23. a) The distance between y = 7 and y = –11 is 18
(these are horizontal lines. Count the units it takes to get to one from the other)
b) The distance between x = –3 and x = –9 is 6
(these are vertical lines. Count the units it takes to get to one from the other)