Download 09 * 6d Angles

These are examples of adjacent angles.
80º
45º
35º
55º
130º
85º
20º
50º
These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º
Add up to 180º.
40º
120º
60º
Adjacent and
Supplementary Angles
140º
Add up to 90º.
20º
20º
70º
Adjacent and
Complementary Angles
70º
•
Definition: A line that intersects two or more lines in a
plane at different points is called a transversal.
•
When a transversal t intersects line n and m, eight angles
of the following types are formed:
Exterior angles
Interior angles
Consecutive interior angles
Alternative exterior angles
Alternative interior angles
Corresponding angles
m
n
t
Corresponding Angles: Two angles that occupy
corresponding positions.
The corresponding angles are the ones at the same location
at each intersection
26
3
7
15
1
3
5
7
4
8
2
4
6
8
Same location different intersections
7

Alternate Interior Angles: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
 3   6,  4   5

Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal.  2   7,  1   8
1
3
5
7
2
4
6
8
Lesson 2-4: Angles and Parallel
Lines
8
In the figure below, triangle ABC is a right triangle and quadrilateral
CDEF is a square.
33
79
??
68
180 – 68 - 33 =
79 degrees
2?
Lines AB and CD are parallel. If
Angle 1 measures 148°, what is the
measure of Angle 2?
180 – 148 = 32 degrees
50



50
Must be intersecting lines
The angles are across from
each other sharing the same
lines.
VERTICAL ANGLES ARE CONGRUENT (EQUAL)
130
130
??
55
80
180 – 63 – 72 = 45
Vertical Angles are congruent
180 – 80 – 45 = 55
45
45
45
63
72

Angle F & J are corresponding
same location different intersections
Corresponding Angles are congruent/equal
if there are parallel lines.
Angle K and G are corresponding
Angle H and L are corresponding
Angle I and M are corresponding
Angle J is 111 degrees

Two parallel lines, one transversal. Criss
Cross on the transversal and outside the
parallel lines.
Angle 7 & 2 are alternate exterior therefore
they are also congruent (equal
measurements)
Angle 7 = 41degrees
Angles 1 & 8 are also alternate interior to each other

Two parallel lines, one transversal. Criss
Cross on the transversal and inside the
parallel lines.
Angle 5 & 4 are alternate exterior therefore
they are also congruent (equal
measurements)
Angle 4 = 146 degrees
Angles 3 & 6 are also alternate interior to each other
Angle 6 & 7 are vertical angles
Vertical angles are congruent
Angle 7 = 36
Sides
 Scalene – no sides equal length
 Isosceles – 2 sides equal length, base angles
are equal
 Equilateral – all three sides are equal length
Angles
 Acute – all three angles are less than 90
degrees
 Obtuse – one angle is greater than 90
degrees
 Right – one angle equals 90 degrees
??
33
57
Left Triangle 180 –33-90= 57
55
90
Right Triangle 180 –35-90= 55
35
33+55 =
88 degrees
Congruent
Top Triangle 180 –36-90= 54
Bottom Triangle 180 –36= 144 / 2 = 72
36
55
72
36
72+54 =
126 degrees

Two sides are equal & the base angles are
also equal.
60
??
Equilateral Triangle – all angles are equal
180 / 3 = 60 degrees
Equilateral Triangle – all angles are equal
180 / 3 = 60 degrees
Circle is 360 degrees
60 + 90 + 60 + x =360
210 + x = 360
-210
-210
X = 150
45
60
45