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Need help on number 5
asked
Sep 10, 2021
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3
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Need help on number 5
Mathematics
middle-school
Mohsan
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Mohsan
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1
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6
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is always true
because angle 1 and angle 4 form a straight line. They are supplementary angles.
is the same as
which is
always true
since these two angles are vertical angles.
is
sometimes true
. There are many cases where it is not true, but it's not impossible for lines z and y to be perpendicular.
is
always true
as these are alternate exterior angles. You can use a few options to prove this, but one way is to use angle 2 = angle 4 (vertical angles) and then angle 4 = angle 8 (corresponding angles). By the transitive property, angle 2 = angle 8.
Angles 1 and 3 are congruent, so we can replace
with
, and we can replace angle 4 with angle 2 as well, going from this
to this
. Next, rearrange things to get
and that solves to
. So the original claim is
sometimes true
. It all depends on if angles 1 and 2 are the same measure or not.
Mert Inan
answered
Sep 17, 2021
by
Mert Inan
8.2k
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