Given: ΔABC

Prove: The sum of the interior angle measures of ΔABC is 180°.






1. Let points A, B, and C form a

triangle.


given


2. Let be a line passing

through B, parallel to ,

with angles as labeled.


defining a parallel line and labeling angles


3.




4. m∠1 = m∠4, and

m∠3 = m∠5.


Congruent angles have equal measures.


5. m∠4 + m∠2 + m∠5 = 180°


angle addition and definition of a straight angle


6. m∠1 + m∠2 + m∠3 = 180°


substitution


What is the missing step in this proof?
A.
Statement: ∠4 ≅ ∠5, and ∠1 ≅ ∠3.
Reason: Alternate Interior Angles Theorem

B.
Statement: DE is parallel to AC.

Reason: AB is a transversal cutting DE and AC.

C.
Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.

Reason: Alternate Interior Angles Theorem

D.
Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.
Reason: ∠1 and ∠4, and ∠3 and ∠5 are pairs of supplementary angles.