Download Complementary Supplementary Angles.jnt

GEOMETRY
Congruent Supplements and Congruent Complements
PROOF
Notes/Practice
GOAL: Be able to recognize complementary and supplementary angles as well as
apply their theorems and use them in proof.
Warm up: Fill the given information into the figure!
C
Given:
 BFC  2 x , CFD  3 y
B
D
BF  DF , BFA  y, DFE  4 x
Find:
DFE
A
F
mDFE  __________
Proving a THEOREM:
Ex 1: Given: EOA is supplementary with AOB
EOA is supplementary with EOD
Prove: AOB  EOD
STATEMENTS
REASONS
E
GEOMETRY
Congruent Supplements and Congruent Complements
PROOF
Notes/Practice
CONGRUENT SUPPLEMENTS THEOREM: If _________ angles are
____________________________ to the same angle, then __________________ are
____________________.
REASON IN PROOF: ______________________________________________________
Theorem that follows from above: If _____________ are _______________________
to _________________________ angles, then they are ______________________.
REASON IN PROOF: ___________________________________________
Ex. 2 – You try!! 
 
Given: QS  TR
POA is a right angle
Pr ove : QOA  TOP
STATEMENTS
O
REASONS
CONGRUENT COMPLEMENTS THEOREM: If _________ angles
are_______________________ to the same angle, then __________________ are
____________________.
REASON IN PROOF: ______________________________________________________
GEOMETRY
Congruent Supplements and Congruent Complements
PROOF
Notes/Practice
Theorem that follows from above: If _____________ are _______________________
to _________________________ angles, then they are ______________________.
REASON IN PROOF: ______________________________________________________
Ex 3: Given: 5 and 6 are supplementary
7 and 8 are supplementary
R
O
5
S
6
7
6  7
Prove: 5  8
Y
STATEMENTS
REASONS
Ex 4: ALGEBRAICALLY USING; Solve for x and y.
A
D
( y  x )
2x
B
( y  x)
C
E
8