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

I just did the test and got 100%

Answer 2

Answer:

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

Reason:Alternate Interior  Angles Theorem

Step-by-step 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.