Geometric Proofs Involving Complementary and Supplementary

Geometric Proofs
Involving Complementary
and Supplementary
Angles
October 18, 2010
SWBAT: Recognize complementary and supplementary angles and prove angles
congruent by means of four new theorems.
Warm - Up
SWBAT: Recognize complementary and supplementary angles
and prove angles congruent by means of four new theorems.
SWBAT: Recognize complementary and supplementary angles and
prove angles congruent by means of four new theorems.
Given:
Prove:
TVK is a right angle.
1 is complementary to
2.
SWBAT: Recognize complementary and supplementary angles and
prove angles congruent by means of four new theorems.
Given:
Prove:
TVK is a right angle.
1 is complementary to
2.
Statements
1.
2.
TVK is a right angle.
m
TVK = 90
3.
1 +
2 =
4.
1 +
2 = 90
5.
TVK
1 is complementary to
Reasons
1. Given
2. A right angle measures
90
3. Angle Addition Postulate
4. Substitution
5.
2. Definition of Complementary
s
SWBAT: Recognize complementary and
supplementary angles and prove angles congruent by
means of four new theorems.
Given:
Prove:
ABC is a straight angle
1 is supplementary to 2.
1
A
B
2
C
SWBAT: Recognize complementary and
supplementary angles and prove angles congruent by
means of four new theorems.
1
Given:
Prove:
ABC is a straight angle A
1 is supplementary to 2.
2
B
1.
Statements
Reasons
ABC is a straight angle 1. Given
2.
1 +
3.
2 =
C
ABC
2. Angle Addition Postulate
1 and
2 form a
Linear pair
3. Definition of Linear Pairs
4. 1 is supplementary to
2 4. Linear Pairs form
supplementary angles.
SWBAT: Recognize complementary and supplementary angles and prove
angles congruent by means of four new theorems.
SWBAT: Recognize complementary and supplementary angles and prove
angles congruent by means of four new theorems.
SWBAT: Recognize complementary and supplementary angles and prove
angles congruent by means of four new theorems.
1.
2.
Statements
1 is complementary to
2 1. given
3 is complementary to
2
1
3
Reasons
2.
Complements Theorem
SWBAT: Recognize complementary and supplementary angles and prove
angles congruent by means of four new theorems.
SWBAT: Recognize complementary and supplementary angles and
prove angles congruent by means of four new theorems.
Given:
Prove:
1.
2.
1
2
4
3
1
Statements
1
4
3
2
4
Reasons
1. given
1 and
2 form a
Linear pair
2. Definition of Linear Pair
3 and
4 form a
Linear pair
3.
1 is suppl. to
3 is suppl. to
4.
2
3
2
4
3. Linear Pairs form
Supplementary angles.
4.
Supplements Theorem
SWBAT: Recognize complementary and supplementary angles and prove
angles congruent by means of four new theorems.
K
R
P
O
M
Statements
Reasons
1. given
1.
2.
3.
4.
KMR
POR
KMO and POM are
right angles
KMO
KMO -
KMR
2. Definition of
3. All right Angles are
POM
POM -
lines
RMO
4. Subtraction Property (3, 1)
5.
RMO
ROM
5. Substitution Property
6.
ROM
RMO
6. Symmetric Property
K
Statements
M
3.
P
Reasons
O
1. given
1.
2.
R
KMR
POR
KMO is a right angle
POM is a right angle
KMO
POM
2. Definition of
3. Right
90
90
to 90
4.
KMR + RMO
POR + ROM
5.
KMR +
POR +
5.
KMR is compl. to RMO 5. Definition of Complementary
POR is compl. to ROM
6.
ROM
RMO
ROM
RMO
KMO
POM
s are
lines
90
90
4. Angle Addition Postulate
5. Substitution (3 into 4)
6.
Complements Theorem
s