The document analyzes five conditions to determine which lines are parallel: a) No lines are parallel as ∠2 and ∠7 are vertical angles. b) Lines t and s are parallel as ∠15 and ∠10 are congruent alternate interior angles. c) Lines m and p are parallel as ∠8 and ∠11 are supplementary interior angles. d) No lines are parallel as four lines are needed to form the angles. e) Lines m and p are parallel as ∠13 and ∠17 are congruent corresponding angles.

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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
b) ∠15 ≅ ∠10
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
b) ∠15 ≅ ∠10
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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s

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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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s

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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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s

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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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s

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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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p
s

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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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p
s

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m
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
∠8 and ∠11 are interior angles on the same side of the transversal
and are supplementary, therefore lines m and p are parallel.
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
∠8 and ∠11 are interior angles on the same side of the transversal
and are supplementary, therefore lines m and p are parallel.
d) ∠20 ≅ ∠5
e) ∠13 ≅ ∠17
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
∠8 and ∠11 are interior angles on the same side of the transversal
and are supplementary, therefore lines m and p are parallel.
d) ∠20 ≅ ∠5
We need four lines to form these angles.
e) ∠13 ≅ ∠17
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s

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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
∠8 and ∠11 are interior angles on the same side of the transversal
and are supplementary, therefore lines m and p are parallel.
d) ∠20 ≅ ∠5
We need four lines to form these angles.
Therefore, no lines are parallel.
e) ∠13 ≅ ∠17
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m
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
∠8 and ∠11 are interior angles on the same side of the transversal
and are supplementary, therefore lines m and p are parallel.
d) ∠20 ≅ ∠5
We need four lines to form these angles.
Therefore, no lines are parallel.
e) ∠13 ≅ ∠17
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m
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
∠8 and ∠11 are interior angles on the same side of the transversal
and are supplementary, therefore lines m and p are parallel.
d) ∠20 ≅ ∠5
We need four lines to form these angles.
Therefore, no lines are parallel.
e) ∠13 ≅ ∠17
Lines m and p with transversal s form these angles.
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Example: Which lines (if any) must be parallel under the
given conditions:
a) ∠2 ≅ ∠7
We can see only two lines are needed to form these angles
∠2 and ∠7 are vertical angles which are always congruent,
therefore no lines are parallel
b) ∠15 ≅ ∠10
Lines t and s with transversal t form these angles.
∠15 and ∠10 are congruent alternate interior angles
Therefore, lines t and s are parallel.
c) ∠8 supplementary to ∠11
Lines m and p with transversal t form these angles.
∠8 and ∠11 are interior angles on the same side of the transversal
and are supplementary, therefore lines m and p are parallel.
d) ∠20 ≅ ∠5
We need four lines to form these angles.
Therefore, no lines are parallel.
e) ∠13 ≅ ∠17
Lines m and p with transversal s form these angles.
∠13 and ∠17 are congruent corresponding angles
Therefore, lines m and p are parallel.
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