Download 1.2A Lesson: Constructing a Copy of an Angle Naming Angles and

1.2A Lesson: Constructing a Copy of an Angle Naming Angles and Parts of an
Angle
Explore: Constructing a Copy of an Angle
Start with a point X and use a compass and straightedge to construct a copy of  S.
Steps on Constructing a Copy of an Angle
A. Use a straightedge to draw a ray with endpoint 𝑋.
B. Place the point of your compass on S and draw an arc that intersects both sides
of the angle. Label the point 𝑠 of intersection 𝑇 and 𝑈.
C. Without adjusting the compass, place the point of the compass on 𝑋 and draw
an arc that intersects the ray. Label the intersection 𝑌.
D. Place the point of the compass on 𝑇 and open it to the distance 𝑇𝑈.
E. Without adjusting the compass, place the point of the compass on 𝑌 and draw
an arc.
a. Label the intersection with the first arc 𝑍.
F. Use a straightedge to draw ⃗⃗⃗⃗⃗
𝑋𝑍
Example 1: Copy the given angles.
Naming Angles and Parts of an Angle
An ____________ is formed by two rays with the same endpoint. The common endpoint is the
_____________ of the angle. The rays are the ____________ of the angle. One way to name an angle is by using
___________ letters. The middle letter is always the ___________.
Example 2: Name the given angle.
A.
Name the angle  ________, ________, or ________
The vertex of the angle is point _____. The sides of the angle are
two rays with common endpoint ______. So, the sides of the angle
are ________ and ________.
B.
Name the angle  ________, ________, ________, or ________
The vertex of the angle is point _____. The sides of the angle are
two rays with common endpoint ______. So, the sides of the angle
are ________ and ________.
Reflect: Without seeing a figure, is it possible to give another name for  MKG? If so, what is it? If not, why not?
_______________________________________________________________________________________
C. Name ∠2in as many different ways as possible.
D. Use a compass to copy ∠𝐵𝐸𝐶.
Naming Angles and Parts of an Angle
Angles are measured in _______________. Angles that have the same measure are called _______________ angles.
The measure of an angle is written as _____________.
You can classify angles by their measures.
Adjacent
Angles
Two angles that have a common
_____________ and a common
___________.
Complementary Angles
A pair of complementary angles has a
sum of ______.
Supplementary Angles
(Linear Angles)
A pair of supplementary angles has a
sum of ______.
Example 3:
A. Find the complementary and supplementary angles.
Complementary angle.
1) 20° ________
2) 35° ________
3) 67° ________
Supplementary angle.
6) 34° ________
4) 80° ________
5) 65° ________
B. Two angles are complementary. One angle has a measure of 4𝑥 + 3 while the other has a measure of
2𝑥 + 21. Find the measure of the smaller angle.
Example 4: Measuring Angles Using a Protractor
A. Measure each angle formed between a pair of rays using a protractor.
1) Angle: _________
2) Angle: _________
B. Find the measure of each angle.
B
C
X
Y
Z
A
Q
1) 𝑚∠𝐴𝑄𝐵 = ________
2) 𝑚∠𝐴𝑄𝐶 = ________
3) 𝑚∠𝑋𝑄𝐴 = ________
4) 𝑚∠𝐴𝑄𝑌 = ________
5) 𝑚∠𝑍𝑄𝑌 = ________
6) 𝑚∠𝑍𝑄𝑋 = ________
C. Use a protractor to determine the measure of each angle. Then classify each angle as acute, right, obtuse, or
straight.
1)
2)
3)
𝑚∠𝐴𝐵𝐶 = ________
𝑚∠𝐷𝐸𝐹 = ________
𝑚∠𝐾𝐿𝑀 = ________
__________________
__________________
__________________