4/15 simplified I need help explain in the answer (so I get how to simplify it)
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From the information in the diagram found in a similar question online (please see attached drawing), the parallel lines are;
- w||z
- x||y
- x||y
- w||z
- w||z
- x||y
- x||y
- w||z
- x||y
- w||z
Parallel lines are lines that do not meet, when extended indefinitely.
The possible information given as obtained from a similar question posted online are;
1. ‹1 is congruent to ‹5
2. ‹7 is congruent to ‹9
3. m‹8 + m‹9 = 180°
4. ‹16 is congruent to ‹14
5. m‹1 + m‹4 = 180°
6. ‹3 is congruent to ‹13
7. ‹2 is congruent to ‹10
8. ‹11 is congruent to ‹15
9. m‹4 + m‹13 = 180°
10. ‹8 is congruent to ‹6
1. Given that ‹1 is congruent to ‹5 where ‹1 and ‹5 are alternate exterior angles, we have that line <em>w </em>is parallel to line <em>z </em>
- w||z
Theorem (converse); Alternate exterior angles formed by two parallel lines having a common transversal are congruent.
2. ‹7 and ‹9 are alternate interior angles.
Given that ‹7 is congruent to ‹9, therefore;
Line <em>x</em> is parallel to line <em>y</em>
- x||y
Theorem (converse); Alternate interior angles formed by two parallel lines having a common transversal are congruent.
3. Given that m‹8 + m‹9 = 180°, therefore;
‹8 and ‹9 are supplementary angles, formed between lines <em>x </em>and <em>y</em>.
‹8 and ‹9 are also consecutive interior angles.
Theorem (converse); Consecutive interior angles formed between parallel lines are supplementary.
Therefore;
- x||y
4. ‹16 and ‹14 are corresponding angles formed by lines <em>w </em>and <em>z</em>.
Theorem (converse); Corresponding angles formed by parallel lines are congruent.
Given ‹16 congruent to ‹14, we have;
- w||z
5. m‹1 and m‹4 are consecutive exterior angles formed by lines <em>w </em>and <em>z</em>.
Theorem (converse); Consecutive exterior angles formed by two parallel lines are supplementary.
Given that m‹1 + m‹4 = 180°, we have;
- w||z
6. ‹3 and ‹13 are alternate exterior angles formed by lines <em>x </em>and <em>y</em>.
Theorem (converse); Alternate exterior angles formed by parallel lines are congruent.
Given that ‹3 congruent to ‹13, we have;
- x||y
7. ‹2 and ‹10 are corresponding angles formed by lines <em>x </em>and <em>y</em>
Given that ‹2 congruent to ‹10, therefore;
- x||y
8. ‹11 and ‹15 are alternate interior angles formed by lines <em>w </em>and <em>z</em>.
‹11 is congruent to ‹15, therefore;
- w||z
9. ‹4 and ‹13 are consecutive exterior angles formed by lines <em>x </em>and <em>y</em>
m‹4 + m‹13 = 180°, therefore;
- x||y
10. ‹8 and ‹6 are corresponding angles formed by lines <em>w </em>and <em>z</em>.
‹8 is congruent to ‹6, therefore;
- w||z
Learn more about angles formed by parallel lines that have a common transversal here:
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