Select the correct answer.
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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Proving Theorems about Triangles: Mastery Test
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