Given: δabc
prove: the sum of the interior angle measures of δabc is 180°.

statement

reason

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: is parallel to .

reason: is a transversal cutting and .

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.