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
- 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
- List two pairs of vertical angles.
- List all the pairs of congruent segments.
- List two linear pairs that do not haveHas the vertex.
- List a right angle.
- List two pairs of adjacent angles that are NOT linear pairs.
- What is the perpendicular bisector ofAE?
- List two bisectors ofMP.
- List a pair of complementary angles.
- IfGCis an angle bisector of^6 AGE, what two angles are congruent?
- 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.
- Angle Addition Postulate
- Substitution