Download 3-1 - Nutley Public Schools

andand
Angles
3-1
Lines
Angles
3-1 Lines
3-2
Theorems
about
Perpendicular Lines
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Warm up:
1. Name two things in the room that are parallel to each
other.
2. Name two things in the room that are skew to each
other.
3. Name two things in the room that are perpendicular to
each other.
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Objective: Use theorems
about perpendicular lines.
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Theorem 3.1:
congruent
All right angles are ______________________.
o
o
m<B=90
m<A=90 and ________________, then
If ________________
~
<A=<B
___________________________.
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Theorem 3.2: If two lines are perpendicular, then they
4 right angles
intersect to form _____________________________.
n m
If ________________,
then ____________, __________,
o
m<1=90 m<2=90
o
T
m<4=90
m<3=90
___________, and _____________.
o
Holt Geometry
o
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Step 1: Mark up ANY angle that you KNOW is a right angle.
Holt Geometry
Congruent - 90
Congruent - 90
Not congruent
Congruent - 90
Not congruent
Congruent - 90
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Theorem 3.3: If two lines intersect to form adjacent congruent
perpendicular
angles, then the lines are ____________.
AC
T
~
BD
<1=<2
If ________________,
then ________________.
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Theorem 3.4: If two sides of adjacent acute angles are
perpendicular, then the angles are ____________.
complementary
o
EF
EH
If ________________, then m<3+m<4=90
____________________.
T
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
We learned from Theorem
3.3 that if two lines
intersect to form adjacent
angles that are
congruent, then the
angles are right angles.
Yes, they are right angles.
Holt Geometry
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
Ask yourself
1) Are the angles REALLY congruent?
2) What is the SUM of the angles?
6y + 30 = 90
-30 - 30
6y = 60
6
6
y =10
Holt Geometry
3-1 Lines and Angles
5x = 90
5 5
x =18
36 + 9y = 90
-36
- 36
9y = 54
9
9
y=6
Holt Geometry
z + z = 90
2z = 90
2
2
z = 45
and Angles
3-1 Lines
3-2
Theorems
about Perpendicular Lines
10. Define perpendicular lines.
Lines that intersect to form
a 90 degree angle.
Holt Geometry
3-1 Lines and Angles
60 + x = 90
x = 30
Holt Geometry
x + 55 = 90
x = 35