aTM UNIT
This is a review of the ATM unit on angles. Many concepts from these unit are reused from the last unit (BFF) except now the concepts are being applied to angles rather than lines or line segments.
ATm 01
- Labeling Angles-Angles can be labeled several ways. Looking at the image below, you could label the angle, angle ABC, angle CBA, angle a, or angle B. When using 3 points, the middle point has to be the vertex. Angle B is the least effective one because if there was an adjacent angle, it would be too confusing to understand which angle you are talking about. Also, you could label an angle by a number (if applicable).
- Points are on the exterior of an angle if they are on the outside of the angle and they are on the interior if they are on the inside of the angle (see diagram). In the first image, B is the vertex.
- Terms
- Congruent Angles-Angles that have equal measures
- Adjacent Angles-2 angles in a plane that have a common vertex and a common side but no common interior points
- Angle Bisector-ray that divides angle into two congruent adjacent angles
ATM 02
This video will show you how to use a protractor if you don't know how to use a protractor to measure an angle, or given a measurement, make an angle.
All you have to do is align the small circle of the protractor with the vertex of your angle, and align one of the rays with the ray on your protractor. Extend the other ray if you need to see it better, and measure the angle, or if you are making an angle, put a mark above the degree you want for your angle and connect it to the vertex. |
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ATM 03
Classifying Angles
- Zero-Measures exactly 0 degrees
- Acute-Measures between 0 and 90 degrees
- Right-Measures exactly 90 degrees
- Obtuse-Measures between 90 and 180
- Straight-Measures exactly 180 degrees
- Reflex-Measures between 180 and 360 degrees
ATM 04
Angle Addition Postulate: If ray B is on the interior of angle AOC, then measure of angle AOB + measure of angle BOC = measure of angle AOC
ATM 05
Notations for Congruencies and Equalities in Angles-Know how to differentiate between the two
*Helpful video |
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ATM 06
Angle Bisector
- First create a reference arc that is more than halfway past the middle of your original angle using a compass with the point on the vertex.
- Then, put your point on one of the intersecting points made by the reference arc and extend your compass more than halfway across the arc so that you can create another arc in the interior of your circle
- Repeat step 2 for the other side.
- You should end up with 3 collinear points on the interior
- Connect them to create your angle bisector
ATM 07
Angle Overlap Theorem
It states that if angle AEB is congruent to angle CED, the angle AEC is congruent to BED.
This could also be written as if angle AEC is congruent to BED, then angle AEB is congruent to CED.
It states that if angle AEB is congruent to angle CED, the angle AEC is congruent to BED.
This could also be written as if angle AEC is congruent to BED, then angle AEB is congruent to CED.
ATM 08
Derive the Angle Overlap Theorem
ATM 50
Construct two congruent angles
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ATM 51
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Angle Addition
Making an angle addition using contraction techniques is quite simple. All you need to do is do the same steps from ATM 51, but repeat it to create a second angle that is adjacent to the first one. This video will explain it |
ATM 52
Angle Bisector
*See ATM 06
*See ATM 06