HELP!!!! Which of the following statements must be true to prove lines m and n are parallel? Question 19 options: A) ∠1 ≅ ∠6 B) m∠3 + m∠5 = 180° C) m∠2 + m∠6 = 180° D) ∠4 ≅ ∠8

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MarvelLoverBarnesidn MarvelLoverBarnesidn

05-08-2022
Mathematics

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HELP!!!! Which of the following statements must be true to prove lines m and n are parallel? Question 19 options: A) ∠1 ≅ ∠6 B) m∠3 + m∠5 = 180° C) m∠2 + m∠6 = 180° D) ∠4 ≅ ∠8

Sagot :

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Eunice1234idn Eunice1234idn · Answer 1 · 2022-08-05T01:18:53-04:00

Answer: B) m∠3 + m∠5 = 180°

Step-by-step explanation:

Concept:

For this question, we will be looking at each answer choice and eliminating the incorrect ones

A) ∠1 ≅ ∠6

∠1 is an exterior angle

∠6 is an interior angle

They are in an alternative position

Since they are neither both exterior nor interior, they are not congruent

[tex]\large\boxed{FALSE}[/tex]

B) m∠3 + m∠5 = 180°

∠3 is an interior angle

∠5 is an interior angle

They are in a same-side position

Since they are both interiors, they fulfill the same-side interior angle theorem, which states: that if a transversal cuts two parallel lines, then the interior angles on the same side of the transversal are supplementary, which means their sum adds up to 180°.

[tex]\Huge\boxed{TRUE}[/tex]

C) m∠2 + m∠6 = 180°

∠2 is an exterior angle

∠6 is an interior angle

They are in a same-side position

Since they are on the same side, they fulfill the corresponding angle theorem which states: the angles that occupy the same relative position at each intersection are congruent to each other.

However, they are only congruent, they don't add up to 180°

[tex]\large\boxed{FALSE}[/tex]

D) ∠4 ≅ ∠8

∠4 is an interior angle

∠8 is an exterior angle

They are in an alternative position

Since they are neither both exterior nor interior, they are not congruent

[tex]\large\boxed{FALSE}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Sagot :

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