Unit 4 proving lines parallel quiz answer sheet
<3 and <6
same side interior angles
123 degrees
62 degrees
12
m||p by the converse of the same side interior angles theorem
48 degrees
given, verticle angles are congruent, corresponding angles
transitive property
given, verticle angles are congruent, transitive property, alternate interior angles converse
alternate exterior angles, same side interior angles, corrosponding angles
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Sorry, but I cannot provide the answer sheet for the quiz you mentioned as it may be against academic integrity policies. However, I can help you with any specific questions you have about proving lines parallel.
To answer a Unit 4 proving lines parallel quiz, you will need to use several properties and theorems related to angles and parallel lines. Here is how you can obtain the answers:
1. <3 and <6:
To determine the relationship between angles <3 and <6, you need to look for angle pairs that have a specific relationship. In this case, you are asked to find "same side interior angles." Same side interior angles are two angles that are on the same side of the transversal and inside the two parallel lines.
To find the measures of <3 and <6, you need additional information, such as the measures of other angles or the presence of any congruent angles. Without more details, it is not possible to determine the exact measures of <3 and <6.
2. 123 degrees:
The measure of 123 degrees is not related to the previous question or any of the properties or theorems mentioned in the prompt. Therefore, we cannot determine how this value is relevant to proving lines parallel.
3. 62 degrees:
Similarly, the measure of 62 degrees is not related to the previous question or any of the properties or theorems mentioned in the prompt. Therefore, we cannot determine how this value is relevant to proving lines parallel.
4. 12:
The number 12 does not seem to have any relevance to proving lines parallel based on the information provided. Without additional context or information, it is difficult to determine its significance.
5. m||p by the converse of the same side interior angles theorem:
To prove that lines m and p are parallel using the converse of the same side interior angles theorem, you would need to show that the same side interior angles are congruent. If you are given that the same side interior angles are congruent, you can conclude that the lines are parallel.
6. 48 degrees:
The measure of 48 degrees is not directly related to the previous question or any of the properties or theorems mentioned in the prompt. Therefore, we cannot determine how this value is relevant to proving lines parallel.
7. Given: vertical angles are congruent, corresponding angles:
Based on the given information that vertical angles are congruent and corresponding angles, you can use the transitive property to conclude that the lines are parallel. The transitive property states that if two angles are congruent to the same angle or to congruent angles, then the two angles are congruent to each other.
8. Given: vertical angles are congruent, transitive property, alternate interior angles converse:
From the given information that vertical angles are congruent and using the transitive property and converse of the alternate interior angles theorem, you can conclude that the lines are parallel.
9. Alternate exterior angles, same side interior angles, corresponding angles:
The information provided does not specify a question or statement that can be inferred from these angle sets. Without a specific question or context, it is difficult to determine the relevance of these angle relationships to proving lines parallel.
Remember, it is crucial to have complete information and a clear question or statement to properly answer and explain the process of proving lines parallel.