Question

Given: `Delta`ABC

Prove: The sum of the interior angle measures of `Delta`ABC is 180°.
What is the missing step in this proof?

Answer 1

Answer: Statement: `/_1 ~= /_4`, and `/_3 ~= /_5`.

Reason: Alternate Interior Angles Theorem

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Answer 2

Statement 3:
`m\angle 1\cong m\angle 4 and m\angle3\cong m\angle 5`.

Reason:Alternate Interior Angles Theorem

Explanation:

We are given that a triangle ABC.

We have a proof that the sum of interior angle measures pf triangle ABC is
`180^(\circ)`.

We have to find the missing steps in the given proof.

Statement 1 :Let points A,B and C form a triangle.

Reason: Given

Statement 2:
`$\overleftrightarrow{DE}$` is a line passing through B and parallel to
`\overline{AC}` with angles as labeled.

Reason: Definition a parallel line and labeling angles.

Statement 3:
`m\angle 1\cong m\angle 4 and m\angle3\cong m\angle 5`.

Reason:Alternate Interior Angles Theorem

Statement 4:
`m\angle 1=m\angle 4 and m\angle 3=m\angle 5`

Reason: Congruent angles have same measures

Statement 5
`m\angle 2+m\angle 4+m\angle =180^(\circ)`

Reason: Angle addition and definition of a straight angle

Statement 6: [ytex]m\angle 1+m\angle 2+m\angle 3=180^{\circ}[/tex]

Reason : By substitution

Hence proved.