Download 12/5/11 EQ: What do I know about line and angle relationships

12/5/11
EQ: What do I know about line and angle relationships?
Acute Angle
-measure less than 90 degrees.
Right Angle
-measures equal to 90 degrees.
Obtuse Angle
-measures between 90 and 180 degrees.
Straight Angle
-measures equal to 180 degrees.
Special Pairs of Angles
Vertical Angles
-are opposite angles formed by intersecting lines. They
are congruent.
3
1 and
2 are
1
2
Vertical angles.
4
Adjacent Angles
1 and
-have the same vertex, share a common side, and do not
not overlap. A
2 are adjacent
1
2 C
m ABC = m 1 + m 2
B
Complementary angles -sum of the measures is 90 degrees.
A
ABD and DBC are
50
D complementary angles.
B
40 C m ABD+m DBC = 90 degrees
Supplementary angles -sum of measures is 180 degrees.
C
C and D are supplementary angles.
125
55
m C + m D = 180 degrees.
D
Classify Angles and
Angle Pairs
1
m 1 is greater than 90 degrees so it is obtuse.
130 60 They have the same vertex, share a common side,
and do not overlap so they are adjacent. The sum of the
angles is 180 degrees, straight angle, so they are also
supplementary angles.
Find a Missing
Angle Measure
x
65
1.Write an equation.
2.Solve(inverse op.)
x
38
x + 65 = 90
- 65 -65
x = 25
x + 38 = 180
-38 -38
x = 142
x
These angles are vertical angels so x = 150.
150
n
m
Perpendicular lines
-lines that intersect at right angles.
m
n
Parallel lines
-two lines in a plane that never intersect or cross.
p q
p
q
transversal
-a line that intersects two or more other lines.
56
1 2
3
4
87
Alternate Interior Angles 2 = 8 and 5 = 3
They are on opposite sides of the transversal and inside the other two lines,
are congruent.
Alternate Exterior Angles 4 = 6 and 1 = 7
They are on opposite sides of the transversal and outside the other two
lines, are congruent.
Corresponding Angles 3 = 7 and 2 =
6
They are in the same position on the two lines in relation to the transversal,
are congruent.
3
Find an Angle Measure
1
6
4
5 2
7
8
Find m
Find m
Find m
2 if m 1 = 63 degrees
3 if m 8 = 100 degrees
4 if m 7 = 82 degrees
12/9/11
EQ: What do I know about triangles and angles?
Triangle
-a figure formed by 3 line segments
Angles of a -the sum of the measures of the angles of a triangle is 180 degrees
Triangle
x
72
Find a Missing
R
S
x + 72 + 74 = 180
Angle Measure
x + 146 = 180
1.Write Equation (+)
- 146 -146
2.Solve
T 74
x = 34 degrees
3 Ways to Classify Triangles by Angles
Obtuse
40
65
Acute
70
Right
50
60
3 acute angles
Scalene
no congruent sides
110
1 obtuse angle
30
25
1 right angle
3 Ways to Classify Angles by Sides
Isoscoles
at least 2 congruent sides
Equilateral
3 congruent sides
Classify Triangles
A
K
71
38
60
C
30
B
Y
71
3 acute angles and
1 right angle and
2 congruent sides so.. acute, isosceles
no congruent sides so…right, scalene