Arjun Dalsania
Once you are done going through this power
point you will be able to do all of the following:
• Measure Segments
• Measure Angles
• Classify angles by size
• Name the parts of a degree
• Recognize congruent angles and
segments
Segments
• To measure segments you can use a ruler, meter
stick, etc.
• You can use any unit of measure you want to but the
most common are inches, feet, meters, centimeters
and millimeters.
• To show what segment we are measuring we call the
segment by the two pts. it contains.
•Ex. If a segment contains pts D and W we would
call the segment DW
Angles
• To measure angels we use a protractor.
• The unit of measure to measure an angle is degrees.
Angles
• The size of an angle is how many
degrees the line turns away from the
vertex.
• To the right is a picture of a
protractor measuring an angle
that is 140 degrees.
• When measuring an angle, if you
come back to the point at which you
started after turning in one direction,
then you know the angle is 360
degrees. This can help you in making
an educated guess on the measure of
the angle.
Acute Angle
Right Angle
There are four different types of angles. The four different types
are Acute angles, Right angles, Obtuse Angles, and Straight
Angles.
• Acute Angles- An angle can be classified as acute if its
measure is greater than 0 degrees but less than 90 degrees.
• Right Angles- An angle can be classified as right if it measure
is exactly 90 degrees.
• Obtuse Angles- An angle can be classified as obtuse if its
measure is greater than 90 degrees but less than 180 degrees.
Obtuse
Angle
• Straight Angles- An angle can be classified as straight if its
measure is exactly 180 degrees.
Straight
Angle
A degree of an angle is divided into 60 minutes (’) and each minute is divided into 60
seconds(’’). So if an angle is 35 ½ degrees we say it is 35 degrees and 30 minutes.
Below are more examples of degrees being changed to degrees and minutes.
• Ex. 50.3 degrees = 50 degrees and 18 minutes
• Ex. 40 degrees = 39 degrees and 60 minutes
• Ex. 85 degrees = 84 degrees, 59 minutes and 60 seconds
• Ex. 30 degrees and 30 minutes = 30 ½ degrees
•To do this you have to find the simplified fraction of 30 mins. over 60 mins. since
60 mins. = one degree
To subtract/add degrees you must have them be in the same form.
• Ex. 80 degrees – 40 degrees 28 minutes and 33 seconds.
•To do this change 80 degrees to 79 degrees 59 minutes and 60 seconds and then
subtract seconds from seconds, minutes from minutes, and degrees from degrees.
So 60-33=27 seconds, 59-28=31 minutes, and 79-40=39 degrees. Ergo, your final
answer would be 39 degrees, 31 minutes, and 27 seconds.
• Congruent Angles- Angles that have the same measure
2
1
• In the picture above angle 1 and angle 2 are congruent
so you would write
1
2
•Congruent Segments- Segments that have the same
length.
5 cm
5 cm
• In the picture above segments
__
AB and CD are congruent so
you would write
DF
• To show two angles or two segments are congruent you can
use tick marks that are exactly the same.
1. Classify each of the angles below as acute, right, obtuse or straight.
Then estimate what their measure can be.
A.
B.
C.
Answers- A. obtuse with about 135 degrees B. right with 90 degrees C. acute with
about 45 degrees.
2. What conclusions can you draw about the following angle ABC and angle DEF?
D
A
Answer- They are congruent because
40+50=90 and 58+32=90
B
C
E
F
3. Given: Angle ABC is a straight angle, Angle1 = 2x+40, and Angle2 = 4x+20. Find the
measure of Angle 2
Answer- since angle ABC is a straight angle the sum of
angle 1 and angle 2 is going to be 180.
(4x+20)+(2x+40)=180
since angle 2=4x+20
6x+60=180
angle 2= 4(20)+40
6x=120
angle 2= 100
X=20
Answers- A. Since angle A is
acute its is greater than 0
degrees but less than 90
degrees. (0<angleB<90)
4. Angle A is Acute
A. what are the restrictions on Angle A
B. what are the restriction on X
2x+14
B. 2x+14>0
2x+14<90
2x>-14
2x<76
x>-7
x<38
(-7<x<38)
1. Change 40 ½ degrees to degrees and minutes.
2. Change 35 degrees and 30 minutes to just degrees.
3. A. What is 38 degrees, 22 mins., and 23 secs. + 32 degrees, 20 mins,
and 15 secs.?
B. What is 60 degrees, 23 mins, and 22 secs – 40 degrees, 18 mins, and
17 secs.?
4. Which 2 of the 3 Angles appear congruent?
1
2
3
5. Angle F is Obtuse
A. What are the restrictions on Angle F?
B. What are the restrictions on x?
*Answers on Next Slide*
4x-80
F
1. 40 degrees and 30 minutes
2. 35 ½ degrees
3. A. 70 degrees, 42 mins., and 38 secs.
B. 20 degrees, 5 mins., and 5 secs.
4. Angles 1 and 2
5. A. 90< angle F<180
B. 42.5<x<65
Works Cited
Littell, McDougal, and Houghton Mifflin. Geometry For Enjoyment
and Challenge. new ed.. Evanstan, IL: McDougal, Littell &
Company, 1997.
Pierce, Rod. "Maths is Fun - Privacy Statement" Math Is Fun. Ed.
Rod Pierce. 22 Dec 2007. 31 May 2008
<http://www.mathsisfun.com/Privacy.htm>