Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles...
Transcript of Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles...
![Page 1: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/1.jpg)
Measuring Angles
![Page 2: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/2.jpg)
1. to name and classify angles
2. to measure angles and angle bisectors
![Page 3: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/3.jpg)
An angle is formed by two rays with the same endpoint.
B
A
C
InteriorExterior
The rays are the sides of
the angle. (𝑩𝑨 and 𝑩𝑪).
The endpoint is the vertex of the angle.
![Page 4: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/4.jpg)
Named by:
1. Number inside:
2. Vertex:
3. Point from one ray, vertex, point from other ray
∠ B
∠1
A
C
B
∠ ABC 1
![Page 5: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/5.jpg)
OB
A
125˚
Every ray of an angle (like
𝑂𝐴) can be paired with a real number from 0 to 180 degrees.
𝑶𝑨 is paired with the measurement 125˚
![Page 6: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/6.jpg)
The absolute value of the difference of the real
numbers paired with the rays of the angles.
O B
A
125˚
0˚
When measuring with a protractor, the middle must be at the vertex and that one ray should be lined up with the side of the protractor at zero degrees.
𝒎∠𝑨𝑶𝑩 = 𝟏𝟐𝟓 − 𝟎𝒎∠𝑨𝑶𝑩 = 𝟏𝟐𝟓˚
![Page 7: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/7.jpg)
C
O B
A125˚
60˚
PROTRACTOR POSTULATE EXAMPLE
𝒎∠𝑨𝑶𝑪 = 𝟏𝟐𝟓 − 𝟔𝟎𝒎∠𝑨𝑶𝑪 = 𝟔𝟓˚
![Page 8: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/8.jpg)
Types of Angles:
acute
X˚ < 90˚right
X˚ = 90˚
obtuse
90˚ < x˚ < 180˚straight
X˚ = 180˚
![Page 9: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/9.jpg)
O
AB
C
Given:
m∠AOB = 60˚m∠BOC = 70˚
What is m∠AOC?m∠AOC = 60 + 70m∠AOC = 130˚
If Point B is in the interior of ∠AOC, then 𝑚∠𝐴𝑂𝐵 +𝑚∠𝐵𝑂𝐶 = 𝑚∠𝐴𝑂𝐶.
![Page 10: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/10.jpg)
angles with the same measure
O
AB
C
∠𝑨𝑶𝑩 ≅ ∠𝑩𝑶𝑪
𝒎∠𝑨𝑶𝑩 = 𝒎∠𝑩𝑶𝑪
![Page 11: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/11.jpg)
ray that divides an angle into two congruent angles.
A
O
C
B𝑶𝑩 is the angle bisector of
∠𝑨𝑶𝑪.
![Page 12: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/12.jpg)
Classify each angle as
acute, right or obtuse.
1. ∠𝑋𝑇𝑈: ______
2. ∠𝑆𝑇𝑊: ______
3. Point K is in the interior
of ∠𝐿𝑀𝑁, 𝑚∠𝐿𝑀𝐾 = 52˚, and 𝑚∠𝐾𝑀𝑁 = 12˚. Find
𝑚∠𝐿𝑀𝑁.
![Page 13: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/13.jpg)
Classify each angle as
acute, right or obtuse.
1. 𝑚∠𝑋𝑇𝑈: ______
2. 𝑚∠𝑆𝑇𝑊: ______
3. Point K is in the interior
of ∠𝐿𝑀𝑁, 𝑚∠𝐿𝑀𝐾 = 52˚, and 𝑚∠𝐾𝑀𝑁 = 12˚. Find
𝑚∠𝐿𝑀𝑁.
![Page 14: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/14.jpg)
4. 𝐵𝐷 bisects ∠𝐴𝐵𝐶, , 𝑚∠𝐴𝐵𝐷 =1
2𝑦 + 10 ˚, 𝑚∠𝐷𝐵𝐶 = (𝑦 + 4)˚.
Find 𝑚∠𝐴𝐵𝐶.
5. 𝑚∠𝑊𝑌𝑍 = 2𝑥 − 5 ˚, and
𝑚∠𝑋𝑌𝑊 = (3𝑥 + 10)˚. Find the value
of x.
![Page 15: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/15.jpg)
4. 𝐵𝐷 bisects ∠𝐴𝐵𝐶, , 𝑚∠𝐴𝐵𝐷 =1
2𝑦 + 10 ˚, 𝑚∠𝐷𝐵𝐶 = (𝑦 + 4)˚.
Find 𝑚∠𝐴𝐵𝐶.
5. 𝑚∠𝑊𝑌𝑍 = 2𝑥 − 5 ˚, and
𝑚∠𝑋𝑌𝑊 = (3𝑥 + 10)˚. Find the value
of x.
![Page 16: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/16.jpg)
1. Angles are formed by two rays with the same endpoint.
2. Angles can be classified as acute, right, obtuse, or straight.
3. When an angle is split into pieces, the pieces can be summed to equal the original angle.
4. Congruent angles have equal measures.
![Page 17: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/17.jpg)
Got It: Represents and/or applies to complex/real world situations
Almost There: Represent and/or apply angle addition/congruence with expressions
Moving Forward: Represent and/or apply angle addition/congruence without expressions
Getting Started: Names and classifies angles
![Page 18: Measuring Angles - Mrs. Robinson's Class€¦ · Measuring Angles. 1. to name and classify angles 2. to measure angles and angle bisectors. An angle is formed by two rays with the](https://reader036.fdocuments.us/reader036/viewer/2022062604/5fb866fca943b7036c24a5b6/html5/thumbnails/18.jpg)
Pages 25 – 27:
12 – 18 even;
30, 32, 42, 44, 50