Given: NQ¯¯¯¯¯¯
is an altitude of △MNP
.

Prove: sinMm=sinPp
Triangle M N P with point Q between points M and P. A segment extends from point N to point Q creating right angle N Q P. Segment M N is labeled lowercase p. Segment N P is labeled lowercase m. Segment N Q is labeled lowercase h.



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Statement Reason
NQ¯¯¯¯¯¯
is an altitude of △MNP
. Given
∠NQM
and ∠NQP
are right angles. Definition of altitude
△NQM
and △NQP
are right triangles. Response area
Response area Definition of sine ratio
psinM=h
and msinP=h
Multiplication Property of Equality
psinM=msinP
Response area
psinMpm=msinPpm
Response area
sinMm=sinPp
Simplify.



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