Download Introduction to Angles Notes Part 1: Angle Basics Part 2: Congruent

Introduction to Angles Notes
Part 1: Angle Basics
What is an angle?
Example 1) Naming Angles
Example 2) Measuring and classifying
angles
a) 𝑚𝐷𝐸𝐶 = ____________
b) 𝑚𝐶𝐸𝐵 = ____________
c) 𝑚𝐴𝐸𝐵 = ____________
Congruent vs Equal Round 2
The set of all points between the sides of the angle is the
interior of an angle. The exterior of an angle is the set of
all points outside the angle.
S
interior of the angle
1
R
exterior of the angle
Part 2: Congruent Angles
Angles that have the same measure are congruent angles. A ray that divides an angle
into two congruent angles is called an angle bisector. In the figure,
⃗⃗⃗⃗⃗⃗
𝑃𝑁 is the angle bisector of ∠MPR. Point N lies in the interior of ∠MPR and
∠MPN ≅ ∠NPR.
T
Part 3: Working with Angles
Angle Addition Postulate: If 𝑆 in the interior of
∠𝑃𝑄𝑅, then 𝑚∠𝑃𝑄𝑆 + 𝑚∠𝑆𝑄𝑅 = ∠𝑃𝑄𝑅
Example 3: 𝑚∠𝐴𝐵𝐷 = 37° and 𝑚∠𝐴𝐵𝐶 = 73°. Using the Angle Addition Postulate, find 𝑚∠𝐷𝐵𝐶.
Angle Bisector: is a ray that divides an angle into two congruent
angles.
⃗⃗⃗⃗⃗⃗ and 𝑸𝑹
⃗⃗⃗⃗⃗⃗ are opposite rays.
In the figure 𝑸𝑷
⃗⃗⃗⃗⃗
𝑸𝑺 bisects ∠PQT.
Example 4) If m∠PQS = 3x + 13 and m∠SQT = 6x – 2, find m∠PQT.
Example 5) Sketching Angles with a protractor
a) Sketch a 48° angle.
b) Sketch a 120° angle