Given: ab ≅ cd
∠egc ≅ ∠cgb
prove: ∠agd is complementary to ∠egc.
proof:
statementh reason
1. given
2. m∠egb = 90° definition of perpendicular lines
3. ∠egb = ∠egc + ∠cgb angle addition
4. ∠egc + ∠cgb = 90° transitive property of equality
5. ∠egc is complementary to ∠cgb. definition of complementary angles
6. what is the next step in the given proof? choose the most logical approach.
a.
statement: ∠egc ≅ ∠agd
reason: substitution property of equality
b.
statement: ∠cgb ≅ ∠agd
reason: vertical angles theorem
c.
statement: ∠ega and ∠egb are supplementary.
reason: linear pair theorem
d.
statement: ∠agd and ∠dgb are supplementary.
reason: linear pair theorem