Select the correct answer from each drop-down menu.

Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.

Statement Reason
Points A, B, and C form a triangle. given
Let be a line passing through B and parallel to . definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
m∠1 = m∠4 and m∠3 = m∠5
m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° substitution

Question

03-02-2020
Mathematics

contestada

Select the correct answer from each drop-down menu.

Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°.

Statement Reason
Points A, B, and C form a triangle. given
Let be a line passing through B and parallel to . definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4
m∠1 = m∠4 and m∠3 = m∠5
m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° substitution

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steffimarish steffimarish · Answer 1 · 2020-02-09T07:41:21+01:00

If you read the question you can find it missing some information. By Googling it, you can find the complete question here. https://brainly.com/question/12852445

The given statement m∠1 = m∠4 and m∠3 = m∠5, its reason is Alternate Interior Angle.

Step-by-step explanation:

Let ABC is a triangle and a line DE traverses through the point B.

That results in AC is parallel to DE.

From the diagram, m∠1 and m∠4 is alternate to each other and m∠3 and m∠5 is alternate to each other. Also, they present in the interior position.

According to alternate interior theorem, when a line traverses through two parallel line creates equal angles in the interior sides which the angles will be opposite to each other.

⇒ m∠1 = m∠4 and m∠3 = m∠5. (refer the diagram).

Now let us continue with the proof,

The total angle of the straight line is 180°.

Here the straight line is DE which consists of three angles m∠4, m∠2, m∠5.

⇒m∠4 + m∠2 + m∠5 = 180° .

we know that, m∠1 = m∠4 and m∠3 = m∠5.

Let us substitute in the above equation.

m∠1 + m∠2 + m∠3 = 180°.

Hence proved.

airam2311 airam2311 · Answer 2 · 2021-11-18T18:00:12+01:00

airam2311 airam2311

18-11-2021

Answer:

C. Statement: ∠1 ≅ ∠4, and ∠3 ≅ ∠5.

Reason: Alternate Interior Angles Theorem

Step-by-step explanation: I just took the test and it was correct. please mark me brainiest if you can

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