Provide the missing statements and reasons for the following proof:
1 answer:
The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:
- R2: Definition of corresponding angles
- R3: Corresponding angles postulate
- R5: Supplement Postulate
- S7: m∠1 + m∠3 = m∠2 + m∠3
- S8: m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)
- Supplementary angles, when added together will give us a sum of 180°.
- Linear pair angles and corresponding angles are supplementary.
Thus, to prove that ∠1 is supplementary to ∠3:
We are given that lines m and n are parallel.
∠1 and ∠3 are corresponding angles.
So therefore, ∠1 = ∠3 by the corresponding angles postulate.
∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.
Based on the substitution property, we have the following:
m∠2 + m∠3 = m∠1 + m∠3
m∠1+m∠3=180°
Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.
The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:
- R2: Definition of corresponding angles
- R3: Corresponding angles postulate
- R5: Supplement Postulate
- S7: m∠1 + m∠3 = m∠2 + m∠3
- S8: m∠1 + m∠3 = 180° (∠1 is supplementary to ∠3)
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