Download - Determining which lines are parallel
![Page 1: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/1.jpg)
1 23 4
5 67 8
mn
t
Example: Which lines (if any) must be parallel under the given conditions:
a)
b)
c) supplementary to
d)
e)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 2: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/2.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 3: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/3.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 4: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/4.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 5: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/5.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 6: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/6.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 7: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/7.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 8: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/8.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 9: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/9.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 10: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/10.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 11: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/11.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 12: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/12.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 13: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/13.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 14: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/14.jpg)
1 23 4
5 67 8
mn
t
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)
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 15: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/15.jpg)
1 23 4
5 67 8
mn
t
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.
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s
![Page 16: Determining which lines are parallel](https://reader036.vdocuments.net/reader036/viewer/2022070509/58a344051a28ab62248b52d9/html5/thumbnails/16.jpg)
1 23 4
5 67 8
mn
t
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.
9 1011 1213 14
15 1617 18
19 2021 22
23 24
p
s