Download Proofs with Quadrilaterals CW

Geometry
Name ______________________
Proofs with Quadrilaterals CW
Period ___________
Date ___________
Things to remember when writing a proof…
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Mark your diagram with the given information
Look for the obvious – shared sides, vertical angles, alternate interior angles etc.
What else does this information tell you when you put it together?
o e.g. Can I prove congruent triangles?
What else do I need to be able to prove my statement?
o e.g. Use CPCTC
Use a two-column proof to prove the following:
1. Given: PQRS is a parallelogram
Prove: PQ  RS , QR  PS
Plan for proof:
a.
b.
c.
Statements
Reasons
2. Given: PQRS is a parallelogram
Prove: The diagonals bisect each other
Plan for proof:
a.
b.
c.
Statements
Reasons
3. Given: VWKJ and SJRU are parallelograms
W and R are supplementary
Prove:
Statements
Reasons
4. Given: Regular hexagon JKLMNO
Prove: KON and OKL are right angles
Statements
Reasons
1.
1. Given
2.
2. Polygon Interior Angles Theorem
3.
JOK 
JKO
3.
4.
4. Triangle Sum Theorem
5.
5.
m JOK  m KON  m JON
m JKO  m OKL  m JKL
6.
6.Substitution
7. m KON  90
7.
m OKL  90
8.
8.
5. Given: LORI is a rectangle and LB  OD
Prove: BIRD is an isosceles trapezoid
Statements
Reasons
1. LORI is a rectangle
1.
2.
2.
ILB and
angles
ROD are right
3.
4.
5.
LI  OR
6.
7.
IBL 
3. All right angles are 
4.
5. Given
ROD
6.
7. CPCTC
8.
8. Definition of Parallelogram
9. BIRD is an isosceles trapezoid
9.
6. Given : AE  CF , AE  BD , CF  BD , DE  BF
Prove: ABCD is a
Statements
7. Given:
Prove:
ABCD ,
Reasons
EBCF
EADF
Statements
Reasons