Download LESSON 1-4: ANGLE TERMS

LESSON 1-4: ANGLE TERMS
Date
* Terms and Definitions:
1. Angle: two noncollinear rays with the same endpoint
A
P
B
The point P is in the interior of the angle.
The point Q is in the exterior of the angle.
Q
1
C
The two rays are the sides of the angle. The sides in the above angle are
and
.
Their common point is called the vertex of the angle. The vertex of the angle above is B.
* Naming Angles:
There are several ways to name an angle. The following are the
different ways of naming the above angle using correct notation.
∠ABC or ∠CBA
∠B
∠1
2. Adjacent Angles:
* notice the vertex is the middle letter; when using 3 points
to name an angle you use one point on one side (ray), the
vertex and a point from the other side (ray)
* you can name an angle using only the vertex
* some angles may be named using an assigned number
two angles that share a common vertex and side
A
C
B
D
∠ABC and ∠CBD are adjacent angles; they share side
and vertex B
* When naming adjacent angles, you cannot use the vertex only to name the angles.
* When naming adjacent angles you must use either the numbers labeled for each angle or
three points that form the angle.
3. Vertical Angles: two non-adjacent angles formed by 2 intersecting lines
A
D
B
C
∠ABC and ∠DBE are vertical angles.
E
∠ABE and ∠CBD are vertical angles.
Every angle has a unique degree measure between 00 and 1800.
PROTRACTOR POSTULATE:
* To distinguish between the name of an angle and its measure we place an "m" in
front of the angle name to represent the measure of that angle.
∠ABC
m∠ABC
=> notation for naming the angle
=> notation for the measure of ∠ABC;
4. Congruent Angles:
* If ∠A
THEOREM:
angles that have the same measure;
∠B, then m∠A
m∠ABC equals a value (#)
is the symbol for congruence
* If m∠A = m∠B, then ∠A
m∠B.
∠B
All right angles are congruent.
* This is true because all right angles have equal measure, 90 degrees.
EXAMPLES/PRACTICE:
1. a) Name the angle in four ways.
b) Name the sides of the angle.
c) Name the vertex.
d) Name a point that lies in the interior of the angle.
e) Name a point that lies in the exterior of the angle.
2.
a) Name all pairs of adjacent angles
b) Name all pairs of vertical angles
R
2
1
S
3
4
P
1
Q
T
4. State whether∠1 and ∠2 are adjacent or vertical
angles.
3. Refer to the diagram below to answer each.
B
A
1
C
P
a) Name two angles adjacent to ∠BPC.
b) Name an angle with measure of 900.
c) Find m∠APD, m∠APC and m∠BPD
2
D
1
2