lease Help- In ΔMNO shown below, segment NP is an altitude:
What property or definition is needed to prove that ΔMPN is similar to ΔNPO?
Question 7 options:
1) Transitive Property of Equality
2) Reflexive Property of Equality
3) Definition of an Altitude
4) Definition of Supplementary Angles
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OpenStudy (cntrl_alt_defeated):
anyone?
OpenStudy (paxpolaris):
|dw:1413412130141:dw|
OpenStudy (cntrl_alt_defeated):
do u want a pic of the triangle
OpenStudy (paxpolaris):
sure ..
OpenStudy (cntrl_alt_defeated):
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OpenStudy (cntrl_alt_defeated):
thts the whole question?
OpenStudy (paxpolaris):
We know that N is right angle.
OpenStudy (cntrl_alt_defeated):
yes
OpenStudy (paxpolaris):
so we need the definition of altitude: to show that P makes right angles.
OpenStudy (cntrl_alt_defeated):
how do i find that? (sorry im new to geometry)
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OpenStudy (paxpolaris):
What is definition of Altitude?
OpenStudy (cntrl_alt_defeated):
the height of an object or point in relation to sea level or ground level.
OpenStudy (paxpolaris):
in geometry: The definition of the altitude of a triangle is a line that extends from one vertex of a triangle perpendicular to the opposite side.
OpenStudy (cntrl_alt_defeated):
oh ok
OpenStudy (paxpolaris):
So definition of an Altitude: gives us NPM and NPO are 90 degrees .
that's enough to prove similarity.
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OpenStudy (paxpolaris):
|dw:1413412909329:dw|
OpenStudy (paxpolaris):
If you assume \(m \angle M= x \) degrees:
\[m \angle O= 90-x \]
also, \(m \angle MNP= 90-x \)
and, \(m \angle ONP= x \)
OpenStudy (paxpolaris):
|dw:1413413210461:dw|
OpenStudy (cntrl_alt_defeated):
so how does this answer my question
OpenStudy (paxpolaris):
the answer is 3) Definition of an Altitude.
... since we needed to know that to prove the similarity above.