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

Question

asked May 26, 2019 218k views

2 Answers

Raphael Schaad · Answer 1 · 2019-05-26T16:21:11+0000

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

Reason: Alternate Interior Angles Theorem

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Zoran Pavlovic · Answer 2 · 2019-05-31T17:28:14+0000

Answer:

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.