Given: δabc
prove: the sum of the interior angle measures of δabc is 180°.
state...
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Mathematics, 20.11.2019 17:31 lindsey0456
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.
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