determining which lines are parallel

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Example: Which lines (if any) must be parallel under the given conditions:

a)

b)

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles

b)

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b)

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b)

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles.

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior angles

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles.

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles. and are interior angles on the same side of the transversal and

are supplementary, therefore lines m and p are parallel.

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles. and are interior angles on the same side of the transversal and

are supplementary, therefore lines m and p are parallel.

d)

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles. and are interior angles on the same side of the transversal and

are supplementary, therefore lines m and p are parallel.

d) We need four lines to form these angles.

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles. and are interior angles on the same side of the transversal and

are supplementary, therefore lines m and p are parallel.

d) We need four lines to form these angles. Therefore, no lines are parallel.

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles. and are interior angles on the same side of the transversal and

are supplementary, therefore lines m and p are parallel.

d) We need four lines to form these angles. Therefore, no lines are parallel.

e)

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Example: Which lines (if any) must be parallel under the given conditions:

a) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles. and are interior angles on the same side of the transversal and

are supplementary, therefore lines m and p are parallel.

d) We need four lines to form these angles. Therefore, no lines are parallel.

e) 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) We can see only two lines are needed to form these angles and are vertical angles which are always congruent,

therefore no lines are parallel

b) Lines t and s with transversal t form these angles. and are congruent alternate interior anglesTherefore, lines t and s are parallel.

c) supplementary to Lines m and p with transversal t form these angles. and are interior angles on the same side of the transversal and

are supplementary, therefore lines m and p are parallel.

d) We need four lines to form these angles. Therefore, no lines are parallel.

e) Lines m and p with transversal s form these angles. and 7 are congruent corresponding anglesTherefore, lines m and p are parallel.

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