http://www.ck12.org Chapter 2. Reasoning and Proof
TABLE2.22:(continued)
Statement Reason
m^63 +m^64 = 180 ◦ Definition of Supplementary Angles
5.m^61 +m^62 =m^62 +m^63
m^62 +m^63 =m^63 +m^64 Substitution PoE
6.m^61 =m^63 ,m^62 =m^64 Subtraction PoE7.^61 ∼=^63 ,^62 ∼=^64 ∼=angles have = measures
In this proof we combined everything. You could have done two separate proofs, one for^61 ∼=^6 3 and one for
6 2 ∼= (^6) 4.
Example 2:In the picture^62 ∼=^6 3 andk⊥p.
Each pair below is congruent. State why.
a)^6 1 and^65
b)^6 1 and^64
c)^6 2 and^66
d)^6 3 and^67
e)^6 6 and^67
f)^6 3 and^66
g)^6 4 and^65
Solution:
a), c) and d) Vertical Angles Theorem
b) and g) Same Angles Complements Theorem
e) and f) Vertical Angles Theorem followed by the Transitive Property
Example 3:Write a two-column proof.
Given:^61 ∼=^6 2 and^63 ∼=^64
Prove:^61 ∼=^64