Transcript Ruler & Protractor postulate

Ruler & Protractor
Postulates
Santucci’s Starter:
1. Complete with sometimes, always, or never:
Two lines that lie in parallel planes are ______ parallel.
Two lines in intersecting planes are ___________ skew.
2. Explain the difference between skew and parallel lines.
Ruler & Protractor Postulates
Ruler Postulate
Find AB
-6
-4
A
-2
Protractor Postulate
2
4
B
6
Distance on the x-y plane (1-7)
d 
( x 2  x1 )  ( y 2  y 1 )
2
Ex: Find the distance between (3, -4)
and (5, 6) in simplified, exact form
2
Segment Addition Postulate
• If A, B, and C are collinear and B is
between A & C then
AB + BC = AC
AC = 60 find x and AB
3x - 12
A
2x+8
B
C
Angle Addition Postulate
• If <AOC and <COD are adjacent angles,
m<AOC + m<COD = m<AOD
A
C
D
O
EXAMPLE
m<AOC = x, m<COD = 5x + 4 and m<AOD = 70
find x and m<COD
A
C
D
O
GEOMETRY LESSON 1–4
25. 90; right
33. –2.5, 2.5
58.
6:00, 12:32
26. 135; obtuse
34. –3.5, 3.5
59.
180
27. 34
35. –6, –1, 1, 6
60.
150
61.
30
62.
100
63.
40
31. –4
56–58. Answers may vary.
Samples are given.
64.
80
32. 1
56. 3:00, 9:00
65.
125
57. 5:00, 7:00
66.
125
28. 70
37–41. Peer edit your work.
29. Q
55. about 42°
30. 6
1-4
Midpoints
M is the midpoint of RT. Find RM, MT, and RT.
Try it!
If B is between A and C, find the value of x
and the measure of BC
AB = 3(x + 7)
BC = 2(x – 3)
AC = 50
Using more algebra
If B is between A and C, find the value of x
and the measure of BC
AB = x2 + 20
BC = 3 - x
AC = 17
Bisectors
QN bisects
DNB.
1. Construct AC so that AC
NB.
2. Construct the perpendicular bisector of AC.
3. Construct
RST so that
RST
4. Construct the bisector of
RST.
5. Find x.
6. Find m
DNB.
QNB.
Starters:
1. Find x if ray WR is an angle bisector
2. Ray RT bisects <ARF. m<FRT = 2x+10, m<ARF = 8x+4
Draw a labeled diagram then find x and m<ART.
When done pick up handout & peer edit hw.
HW Answers p. 32
79. 30
70. a.
19.5
b. 43; 137
c.Answers may vary. Sample:
The sum of the measures S/B 180.
71. y = 15; AC = 24,
DC = 12
72. ED = 10, DB = 10,
EB = 20
82. C
83. F
84. D
85. H
86.
79 and 167
75. 12; m AOC = 82,
m AOB = 32,
m BOC = 50
87. never
76. 8; m AOB = 30,
m BOC = 50,
m COD = 30
89. always
77. 18; m AOB = 28,
m BOC = 52,
m AOD = 108
91. always
78. 7; m AOB = 28,
m BOC = 49,
m AOD = 111
93. always
88. never
90. never
92. always
94. never
HW Answers p. 46
7.
25
18.
(4, 2)
35.
43.
5.4; (–2.5, 3)
42.
ST = (5 – 2)2 + (–3 – (–6))2 =
9 + 9 = 3 2 4.2
TV = (6 – 5)2 + (–6 – (–3))2 =
1 + 9 = 10 3.2
The midpts. Are the
same, (5, 4). The
diagonals bisect each
other.
SW = (5 – 6)2 + (–9 – (–6))2 =
9 + 9 = 3 2 4.2
No, but ST = SW and TV = VW.