1-4 measuring segments and angles. ab 5 in postulate 1-5 ruler postulate the point of a line can be...
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1-4 Measuring Segments and Angles
A B5 in
Postulate 1-5 Ruler Postulate
The point of a line can be put into a one-to-one correspondence with the real number so that the distance between any two points is the absolute value of the difference of the corresponding numbers.
AB = | a – b | B A
4 10
Two segments with the same length are congruent.
If AB = CD, then AB ≅ CD
≅ means congruent
B A6 B A
D C6D C
Postulate 1-6 Segment Addition Postulate
If three points A, B, and C are collinear and B is
between A and C, thenAB + BC = AC
A
B
C
Write the Segment Addition Postulate for the points described. Draw a
picture to help.
S is between D and P
C is between Q and R
T is between M and N
For each problem, draw a picture representing the three points and theinformation given. Solve for indicated.
If AC = 24 in. and CE = 13 in., AE = _____.
If CE = 7in. and AE = 23 in., AC = _____.
Find QR in the following problems. R is between Q and S.
If RS = 44.6 and SQ = 68.4, find QR.
If RS = 33.5 and RQ = 80, find SQ.
If GJ = 32,
• find x
• find GH
• find HJ
If AX = 45,
• find y
• find AQ
• find QX
For each problem, draw a picture representing the three points and theinformation given. Solve for indicated.
Given : AC = 39 m
A B C
2x-8 x+17
x = ________
AB = _______
BC = _______
If U is between T and B, find the value of x and the lengths of the
segments. TU = 2x, UB = 3x + 1, TB = 21
x = ______
TU = _______
UB = _______
TU = 4x-1, UB = 2x -1, TB = 5x
x = ______
TU = _______
UB = _______
A midpoint of a segment is a point that divides the segment into two congruent segments.
A B C
M is the midpoint of RT
• find x
• find RM
• find RT
An angle is formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle). Angles are measured in degrees.
Sides are GC and GA; G is the vertex.Name this angle:
G
3
CGA
AGC
AB
DC
O
Angles can be...
Acute: 0 < x < 90
x° x°
Right: x = 90
x°
Obtuse: 90 < x < 180
x°
Straight: x = 180
17
Adjacent AnglesTwo angles are called adjacent angles if they
share a vertex and a common side (but neither is inside the opening of the other).
Angles 1 and 2 are adjacent:
1 2
Postulate 1-8 Angle Addition Postulate
• If point B is in the interior of AOC, then mAOB + mBOC = m AOC.
19
Example
A
M
TH
.m MAH
Angles with the same measure are congruent.
If m1 = m2, then 1 2
Congruent
“curtains”
Homework—
Page 29-33 (1, 3, 8-16, 27, 28, 59, 60, 61, 70-72, 75-78)
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