8. Error Analysis. Find and Correct ALL 3 of the errors in the proof.( 3 points)
Given: m||n
Prove: m<4+m<6=180
m||n Given
<4~=<7 same side interior theorem
m<7+m<6=180 supplementary angels theorem
m<4+m<6=180 transitive property
To find and correct the errors in the proof, let's go through each statement and identify any mistakes:
1. "m||n" - This statement is correct and represents the given information that m is parallel to n.
2. "<4~=<7" - The notation "<4~=<7" is unclear and does not correspond to any known geometry theorem or rule. It seems that there is a typographical error or a mistake in expressing the intended relationship between these two angles. To correct this error, let's assume that we want to use the same-side interior angles theorem to relate the angles. The correct statement could be "<4 and <7 are same-side interior angles."
3. "m<7+m<6=180" - This statement is incorrect because it incorrectly applies the supplementary angles theorem. The supplementary angles theorem states that if two angles are supplementary, then their sum is 180 degrees. However, the given information does not indicate that <7 and <6 are supplementary angles. Therefore, we can't directly conclude that their sum is 180 degrees. To correct this error, we need to use the correct theorem or provide additional information to establish the relationship between <7 and <6.
4. "m<4+m<6=180" - This statement incorrectly claims that it follows the transitive property, which is used to relate the equality of two quantities through an intermediate quantity. However, in this case, we don't have any intermediate quantities or equations to establish the transitive property. Therefore, the use of the transitive property is unjustified.
With these corrections in mind, let's revise the proof:
Given: m||n
Prove: <4 and <7 are same-side interior angles.
m||n Given
<4 and <7 are same-side interior angles Same-side interior angles theorem
By following the same-side interior angles theorem, we can establish the relationship between <4 and <7.