Question

Use the following figure and information to complete the proof. Given: m∠4=m∠2m∠5=m∠3m∠DBE=180∘ Prove: m∠1+m∠2+m∠3=180∘ Parallel lines m & n. Triangle A B C with A & C on n & B on m. A is to the left of C with angle 2 at A & angle 3 is at C. B is above A & C with angles 4 3 & 5 at C from left to right.© 2019 StrongMind. Created using GeoGebra. Match each numbered statement in the proof to its correct reason.

Answer 1

The correct matching of each statement proof to it's reason can be seen in the attached table above.

How to ascertain the correct statement proof to it's reason?

1.) Given that;

m∠4 = m∠2

m∠5 = m∠3

m∠DBE = 180°

2.) m∠4+m∠1+m∠5 = m∠DBE. This is soo because of Angle Addition Postulate because the sum of the three angles is equal to the measure of the angle they form.

3.) Because m∠DBE = 180°,

m∠4+m∠1+m∠5 = 180° (Transitive property of equality).

4.) Because m∠4= m∠2 and m∠5 = m∠3

m∠2 +m∠1+m∠3 = 180°( substitution property of Equality).

5.) m∠1+m∠2+m∠3 = 180° (commutative property of Addition)

Answer 2

Step-by-step explanation:

The given information is

m∠4 = m∠2

m∠5 = m∠3

m∠DBE = 180

The angle addition postulate says that the angle that the sum of the angles 4, 1, and 5 is equal to the angle DBE, so we can write the following equation

m∠4 + m∠1 + m∠5 = m∠DBE

But, we know that m∠DBE = 180, so by transitivity, we get:

m∠4 + m∠1 + m∠5 = 180

Then, we also know that m∠4 = m∠2 and m∠5 = m∠3, so we can substitute the angles to get

m∠2 + m∠1 + m∠3 = 180

Therefore, we can change the order by the commutative property to get

m∠1 + m∠2 + m∠3 = 180

Answer:

So, the answer is