Download 1-4 Measuring Segments and Angles

1-4 MEASURING SEGMENTS AND ANGLES (p. 25-33)
Postulate 1-5: Ruler Postulate
The points of a line can be put into one-to-one correspondence with the real
numbers so that the distance between any two points is the absolute value of the
difference of the corresponding numbers.
Why is absolute value required in the above postulate?
A coordinate is a number associated with a point.
Example: P has a coordinate of -4 and Q has a coordinate of -7. What is the distance
between these two points?
Discuss the difference between AB and AB.
Congruent segments are segments that have the same length.
Example: Sketch two segments that have the same length and show the “is congruent
to” symbol. Use identical tick marks to indicate congruent segments.
The  symbol is a combination of = (meaning same size) and ~ (meaning same shape).
The = sign only compares numbers; it never compares geometric figures.
Do 1 a and b on p. 26.
Postulate 1-6: Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C, then
AB + BC = AC.
Between does not necessarily mean exactly halfway between the two outside points.
One can remember the Segment Addition Postulate by noticing that the sum of the parts
equals the whole.
Example:
A
2x-6
x+7
N
B
If AB = 25, find the value of x. Then, find AN and NB.
Do 2 on p. 26.
A midpoint of a segment is a point that divides a segment into two congruent segments.
A midpoint, or any line, ray, or segment that goes through a midpoint, is said to bisect the
segment.
Example: Sketch a segment that is being bisected by a ray. Label the midpoint M.
Example:
5x+9
R
8x-36
M
T
If M is the midpoint of RT , find RM, MT, and RT.
Do 3 on p. 27.
An angle is formed by two rays with the same endpoint. The rays are the sides of the
angle. The endpoint is the vertex of the angle.
Example: Sketch an angle with three labeled points and a number. Show how to name
this angle by using four different names. Show the symbol for angle.
Example: Make a sketch where three different angles share the same vertex. Why
would it not be appropriate to use the one-letter method to name an angle in this figure?
Simply stated, never name an angle in a way that could potentially confuse the reader.
In our course, angles are measured in degrees. If you see a lowercase m in front of the
angle symbol, the m means “the measure of.”
Example: What does the following statement say in words?
mABC  72.5 or m ABC  72.5
Note: You do not need to write the degree symbol in our course.
Instead of presenting the Protractor Postulate (Postulate 1-7) on p. 28, show students how
to find the measure of an angle by using a protractor. Students can sketch an angle and
measure it with their protractors. Give each student a transparency protractor.
Angles are classified according to their measures.
Angle Name
1. Acute
2. Right
3. Obtuse
4. Straight
Measure
0 < measure < 90
exactly 90
90 < measure < 180
exactly 180
Example: Show the box or square symbol to indicate a right angle.
Postulate 1-8: Angle Addition Postulate
If T is in the interior of CAN, then m CAT  m TAN  m CAN.
This postulate works just like the Segment Addition Postulate, except it pertains to
angles. In other words, the sum of the parts equals the whole.
Example:
A
D
1
2
B
C
Suppose that
here?
m
1  37 and m ABC  82, find
m
2. What simple operation can you use
Example:
G
E
Suppose
F
m
H
EFG  6x and m GFH  2x. Write and solve an equation to find
m
EFG.
Congruent angles are angles with the same measure.
Example: Sketch three angles that appear to have the same measure. Use identical tick
marks to indicate congruence. Write a congruence statement for these three angles.
Homework p. 29-33: 3,7,9,11,15,17,20,27,31,34,36a,44,49,57,60,66,71,78,85,87,93
78. Solve 2(4x  3)  7x  16x - 1
15x  6  16x - 1
x7