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| PAGE: 32 | SET: Exercises | PROBLEM: 111 |
Let the vertices of the triangle be 
, 
, and 
.
Each two vertices form a line segment.
Find the slopes of three sides of the triangle.
The formula for slope is 
.
Find the slope of 
.
Substitute 
for 
, 
for 
, 
for 
and 
for 
in 
.
.
Find the slope of 
.
Substitute 
for , for , 
for and 
for in .
.
Find the slope of 
.
Substitute 
for , 
for , 
for and 
for in .
.
Observe the three side slopes are 
, 
, and 
.
Perpendicular lines slopes are negative reciprocals to each other.
Therefore, the sides of the triangle 
and 
are perpendicular.
Perpendicular lines intersect at right angles to one another.
is a right angle triangle.
Thus, 
, 
, and 
are vertices of right triangle.
, 
, and 
are vertices of right triangle.
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