SOLUTION: Show by means of angles that A=(-1,0), B=(4,6), and C=(10,1) are the vertices of an isosceles triangle.

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Question 970823: Show by means of angles that A=(-1,0), B=(4,6), and C=(10,1) are the vertices of an isosceles triangle.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Show by means of angles that A=(-1,0), B=(4,6), and C=(10,1) are the vertices of an isosceles triangle.
We draw the triangle to see which angles appear to be the base angles.




We would normally use distances to show that AB ≅ AC to show that ABC is
isosceles. But we are instructed not to do it that way, but to show 
instead that ∠A ≅ ∠C.

First we find the slopes of all three sides:

Slope of AB:    
Slope of AC:  
Slope of BC:  

The base angles are acute angles so we use absolute value
to insure that the tangent is positive:



Multiply top and bottom by 55



Now we do that for ∠C:



Multiply top and bottom by 66



So ∠A and ∠C have the same tangents and so they have the same measure
and since the base angles of ΔABC are ≅, ΔABC is isosceles.

Edwin
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