Unit Study #2 (ATM)
ATM01
I can correctly label angles in all possible valid ways. I can correctly identify points on the interior, exterior, and vertex. The angles (above) have a shared ray. Angles COB and BOA are congruent and adjacent angles because they share the ray OB. Ray OB is an angle bisector as well. Opposite rays can be created when there are three points are on a line. The point in the middle is the endpoint of the two opposite rays. The points on each side are the other point on each ray.
ATM02
Given an angle, I can measure it with a protractor. Given an angle measurement, straight edge, and protractor, I can draw an angle with that measurement. Place the angle's vertex on the bottom, center hole. Align one ray on the line extending out from the sides of the hole, and setup the other ray on the protractor. Identify where the angle extends into the protractor's increments.
ATM01
I can correctly label angles in all possible valid ways. I can correctly identify points on the interior, exterior, and vertex. The angles (above) have a shared ray. Angles COB and BOA are congruent and adjacent angles because they share the ray OB. Ray OB is an angle bisector as well. Opposite rays can be created when there are three points are on a line. The point in the middle is the endpoint of the two opposite rays. The points on each side are the other point on each ray.
ATM02
Given an angle, I can measure it with a protractor. Given an angle measurement, straight edge, and protractor, I can draw an angle with that measurement. Place the angle's vertex on the bottom, center hole. Align one ray on the line extending out from the sides of the hole, and setup the other ray on the protractor. Identify where the angle extends into the protractor's increments.
ATM03
A zero angle is made from two overlapping rays. An acute angle is an angle between that has a measurement between 0 and 90. A right angle is an angle with a measurement of 90. An obtuse angle is an angle with a measurement between 90 and 180. A straight angle has a measurement of 180. A reflex angle has a measurement anywhere between 180 and 360.
ATM04
The angle addition postulate: If point B lies on the interior of angle CAD, then
CAB + BAD = CAD.
A zero angle is made from two overlapping rays. An acute angle is an angle between that has a measurement between 0 and 90. A right angle is an angle with a measurement of 90. An obtuse angle is an angle with a measurement between 90 and 180. A straight angle has a measurement of 180. A reflex angle has a measurement anywhere between 180 and 360.
ATM04
The angle addition postulate: If point B lies on the interior of angle CAD, then
CAB + BAD = CAD.
ATM05
To say that an angle has a measurement of degrees, you have to write measurement of angle blank equals that number. To say that to angles are congruent, you simply write the angle symbol and then the angle's name. Any comparison between an angle and a number measurement, you are required to state m, angle symbol followed by the angle name. Angle congruencies are stated as the angle symbol, followed by the angle name.
ATM06
I can correctly sketch an angle bisector with correct labels. You can determine that the
went exactly through the middle due to the construction marks on the line and the two
dashes on each angle, identifying that they are equal.
To say that an angle has a measurement of degrees, you have to write measurement of angle blank equals that number. To say that to angles are congruent, you simply write the angle symbol and then the angle's name. Any comparison between an angle and a number measurement, you are required to state m, angle symbol followed by the angle name. Angle congruencies are stated as the angle symbol, followed by the angle name.
ATM06
I can correctly sketch an angle bisector with correct labels. You can determine that the
went exactly through the middle due to the construction marks on the line and the two
dashes on each angle, identifying that they are equal.
ATM07
The angle overlap theorem states that if (see figure to the left) measurement of angle APD, equals measurement of angle CPB, then measurement of angle APC, equals measurement of CPB.
The angle overlap theorem states that if (see figure to the left) measurement of angle APD, equals measurement of angle CPB, then measurement of angle APC, equals measurement of CPB.
ATM08
How to derive the angle overlap theorem
1. m<MAC = m<PAT
2. m<MAC + m<MAP = m<CAP
3. m<PAT + m<MAP = m<TAM
4. m<MAC + m<MAP = m<TAM
5. m<CAP = m<TAM
ATM50
Construct two congruent angles using a compass.
Use a compass and draw a portion of a circle across angle;
Make a line segment and do the same across segment;
Set compass to the intersected points on the angle;
Do the same with the segment;
Draw line from segment vertex up through intersected arc
How to derive the angle overlap theorem
1. m<MAC = m<PAT
2. m<MAC + m<MAP = m<CAP
3. m<PAT + m<MAP = m<TAM
4. m<MAC + m<MAP = m<TAM
5. m<CAP = m<TAM
ATM50
Construct two congruent angles using a compass.
Use a compass and draw a portion of a circle across angle;
Make a line segment and do the same across segment;
Set compass to the intersected points on the angle;
Do the same with the segment;
Draw line from segment vertex up through intersected arc
ATM51
Construct an angle that is the sum of two given angles. The two original angles are
BAC, and RPQ, to create angle SPQ.
Construct an angle that is the sum of two given angles. The two original angles are
BAC, and RPQ, to create angle SPQ.
ATM52
I can construct an angle bisector of a given angle with
just a compass. Place the compass on the vertex, make arc
across angle. Place compass on point and make arc at least
halfway across, repeat on each side. Place ruler on vertex and
make line through arc intersections. Indicate that the line is in the middle of the angle.
I can construct an angle bisector of a given angle with
just a compass. Place the compass on the vertex, make arc
across angle. Place compass on point and make arc at least
halfway across, repeat on each side. Place ruler on vertex and
make line through arc intersections. Indicate that the line is in the middle of the angle.