Download Perpendicular Lines

October 13, 2015
2.5
Perpendicular Lines
October 13, 2015
2.5
Objectives
1) Apply the definition and theorems about
perpendicular lines.
October 13, 2015
Theorem 2-4
If two lines are perpendicular, then they
form congruent adjacent angles.
On a proof you
would write:
"If 2 lines ⊥, then
they form ≅ adj. ∠'s"
Theorem 2-5
If two lines form congruent adjacent angles,
then the lines are perpendicular.
On a proof you
would write:
"If 2 lines form ≅
adj. ∠'s, then the
lines are ⊥ "
October 13, 2015
Theorem 2-6
If the exterior sides of two adjacent
acute angles are perpendicular, then the
angles are complementary.
On a proof you
would write:
A
B
O
C
"If ext. sides of 2 adj.
acute ∠'s are ⊥, then
the ∠'s are
complementary"
Copy and complete the proof of Theorem 2-5:
If two lines form congruent adjacent angles,
then the lines are perpendicular.
m
1
Given: ∠1 ≅ ∠2
Prove: m ⊥ n
Statement
Reason
2
n
October 13, 2015
Copy and complete the proof of Theorem 2-5:
If two lines for congruent adjacent angles,
then the lines are perpendicular.
m
Given: ∠1 ≅ ∠2
Prove: m ⊥ n
1 2
on
i
t
u
Sol
Statement
Reason
1. ∠1 ≅ ∠2
2. m∠1 + m∠2 = 180
3. m∠2 + m∠2 = 180
4. m∠2
m ⊥ n= 90
5. ___________
Given
1. _________________
Angle Addition Postulate
2. _________________
Substitution
3. _________________
Division Property
4. _________________
5. Definition of ⊥ Lines
GIVEN: AB ⊥ CD
Use the diagram to classify each
statement as true or false.
n
A
E
C
D
G
F
1. AB ⊥ EF
2.
3.
4.
5.
6.
7.
F
T
∠CGB is a right angle
T
∠CGA is a right angle
T
m∠DGB = 90
∠EGC and ∠EGA are complements
∠DGF is complementary to ∠DGA
∠EGA is complementary to ∠DGF
B
T
F
T
October 13, 2015
Name the definition or state the theorem
that justifies the statement about the diagram. (page 1 of 3)
E
D
F
B
A
C
1) If ∠EBC is a right angle, then BE ⊥ AC.
AN
ER
SW
Def. of | lines
2) If AC ⊥ BE, then ∠ABE is a right angle.
AN
ER
SW
Def. of | lines
Name the definition or state the theorem
that justifies the statement about the diagram. (page 2 of 3)
E
D
F
B
A
3) If BE ⊥ AC,
AN
ER
SW
C
(2-6)
If the ext. sides of 2 adj. angles are | ,
then the angles are complementary
then ∠ABD and ∠DBE are complementary
4) If ∠ABD and ∠DBE are complementary angles,
then m∠ABD + m∠DBE = 90
AN
ER
SW
Def. of complementary angles
October 13, 2015
Name the definition or state the theorem
that justifies the statement about the diagram. (page 3 of 3)
E
D
F
B
A
C
5) If BE ⊥ AC, then m∠ABE = 90
AN
Def. of | lines
ER
SW
6) If ∠ABE ≅ ∠EBC, then AC ⊥ BE
AN
ER
SW
(2-5)
If 2 lines form ≅ adjacent
angles, then the lines are |