Download 2.5 Perpendicular Lines

Geometry
2.5 Perpendicular Lines
Perpendicular Lines Definition
Lines Defn. – two lines that intersect to
form right angles
.
JK
MN
M
J
.
K
.
.
L
Segments and rays may also be perpendicular
JK
MN
LJ
LN
JK
ML
.
JK
N
LN
Two Ways to Use the Defn.
1) If JK
MN, then…
each of the 4 angles is a right angle.
2) If any one of the four angles is a right
angle, then…
. M
JK
MN
J
.
K
.
.
L
.
N
Two New Theorems
If two lines are perpendicular, then they form
congruent adjacent angles.
lines form
adj. ' s
If two lines form congruent adjacent angles,
then the lines are perpendicular.
. M
lines
 adj. ' s

Example
If m1  m4 , then….
JK
NM by…
 adj. ' s
J
.
lines
K
1
2
4
3
.
N
.
Theorem
If the exterior sides of two adjacent angles are
perpendicular, then the angles are
complementary.
Ext. sides of 2 adj. ' s
comp. ' s
A
.
If OA
OC, then…
1 and 2 are complementary.
O
B
.
1
.
2
.
C
Let’s Try Some Together
Please open your books to page 57 (#1, 6-11)
1) Given
Defn. of
lines
Defn. of congruent angles
6) Defn. of
lines
7) Defn. of
lines
8)
Lines form
adj. ' s
9) Defn of
lines
10)  adj. ' s
Lines
11) Defn. of
lines

A Few Together from the HW
P. 58-59, Let’s complete #11, #18, and #19
together
HW P.58-59 (#1-25)