Respuesta :

Answer:

∠1 = ∠4 and ∠3 = ∠5  ( alternate interior angle).

Step-by-step explanation:

Given : Triangle ABC with angle  1, 2, 3.

To find : Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.

Solution : We have given that triangle ABC with angle  1, 2, 3.

Here, line DE and AC are parallel and BA is traversal line.

∠1 = ∠4 ( alternate interior angle)

∠3 = ∠5 ( alternate interior angle)

∠4 + ∠2+ ∠5 = 180  ( angle formed on line)

∠1 + ∠2 + ∠3 = 180.

Therefore, ∠1 = ∠4 and ∠3 = ∠5  ( alternate interior angle).

MrRoyal

The angles in a triangle add up to 180 degrees.

The text that completes the proof is: alternate interior angle

From the question, we can see that the missing statement is on the 4th line

Where:

[tex]\angle 1 \cong \angle 4[/tex] and [tex]\angle 3 \cong \angle 5[/tex]

From the figure of the triangle, we can see that:

  • [tex]\angle 1[/tex] and [tex]\angle 4[/tex] are alternate interior angles
  • [tex]\angle 5[/tex] and [tex]\angle 3[/tex] are alternate interior angles

Hence, the statement that completes the proof is: alternate interior angle

Read more about the proofs of angles in a triangle at:

https://brainly.com/question/20441035

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