CK-12 Geometry Concepts

2.8. Two-Column Proofs http://www.ck12.org

TABLE2.25:

Statement Reason

1.^6 Lis supplementary to^6 M,^6 Pis supplementary to

(^6) O

1. Given
   2.^6 L+^6 M=180,^6 P+^6 O= 180 2. Definition of Supplementary Angles
   3.^6 L+^6 M=^6 P+^6 O 3. SubstitutionPoE
   4.^6 L∼=^6 O 4. Given
   5.^6 O+^6 M=^6 P+^6 O 5. SubstitutionPoE
   6.^6 M=^6 P 6. SubtractionPoE

Practice

Write a two-column proof for questions 1-5.

1.Given:^6 MLN∼=^6 OLPProve:^6 MLO∼=^6 NLP

2.Given:AE⊥ECandBE⊥EDProve:^61 ∼=^63

3.Given:^61 ∼=^64 Prove:^62 ∼=^63

4.Given:l⊥mProve:^61 ∼=^62

5.Given:l⊥mProve:^6 1 and^6 2 are complements

Use the picture for questions 6-15.

Given:His the midpoint ofAE,MPandGC

Mis the midpoint ofGA

Pis the midpoint ofCE

AE⊥GC

6. List two pairs of vertical angles.


7. List all the pairs of congruent segments.


8. List two linear pairs that do not haveHas the vertex.


9. List a right angle.


10. List two pairs of adjacent angles that are NOT linear pairs.


11. What is the perpendicular bisector ofAE?


12. List two bisectors ofMP.


13. List a pair of complementary angles.


14. IfGCis an angle bisector of^6 AGE, what two angles are congruent?


15. Fill in the blanks for the proof below.

Given: Picture above and^6 ACH∼=^6 ECH

Prove:CHis the angle bisector of^6 ACE

TABLE2.26:

Statement Reason

1.^6 ACH∼=^6 ECH
CHis on the interior of^6 ACE

1.

2.m^6 ACH=m^6 ECH 2.

3. 
   
   
   
   3. Angle Addition Postulate
   
   
   
   


4. 
   
   
   
   4. Substitution