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.

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. Straight Angles- An angle can be classified as straight if its measure is exactly 180 degrees. Acute Angle Right Angle Obtuse Angle 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 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 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 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? A C B D EF Answer- They are congruent because 40+50=90 and 58+32=90

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)=180since angle 2=4x+20 6x+60=180 angle 2= 4(20)+40 6x=120 angle 2= 100 X=20 4. Angle A is Acute A. what are the restrictions on Angle A B. what are the restriction on X 2x+14 Answers- A. Since angle A is acute its is greater than 0 degrees but less than 90 degrees. (0<angleB<90) 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 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? 5.Angle F is Obtuse A. What are the restrictions on Angle F? B. What are the restrictions on x? 123 4x-80 F *Answers on Next Slide*

1.40 degrees and 30 minutes 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, Pierce, Rod. "Maths is Fun - Privacy Statement" Math Is Fun. Ed. Rod Pierce. 22 Dec May 2008