The triangle is scalene, not isosceles. - Given
In a Scalene triangle no angles or sides are the same. - Def scalene
An Altitude is always perpendicular to the base. - Def Altitude
A line drawn from a vertex that bisects the angle of the two sides can not be perpendicular because... uhrm...
My math deals with physical objects and im used to assigning number to stuff.
ok, lets take a triangle, knows Scalene.
Vertices A, B, and C
^Hah firefawx doesn't have this word in its dictionary.
It Is given that thse three angles can not be equal
A != B
B != C
C != A
Given
Construct a line from Vertex B Perpendicular to line AC, name the new vertex D
Angle ADB = Angle CDB = 90 Degrees
- Constructed
Now,
(Im implying the angle symbol here)
The two angles created by The drawn altitude
ABD = 180 - (ADB + BAC)
CBD = 180 - (CDB + BCA)
Now, we know that ADB and CDB are both equal to 90 degrees
So, we can subtract them.
ABD = 90 - BAC
CBD = 90 - BCA
So, since we are given (Scalene) that BAC != BCA
90 - BAC != 90 - BCA
For the altitude to have "Bisected" the angle the two created angles must be equal, but since (as I just showed) While BAC != BCA ABD CAN NOT EQUAL CBD
So, there's an algebratic proof that the two created angles can not be equal. (Thus they cant bisect)
Ok here's all of my gobblygook removed
Code:
BAC != ABC
CBA != ACB
ACB != BAC
Given, Definition of a scalene triangle.
Line BD is an altitude Perpendicular to AC
ADB = CDB = 90 Degrees
Definition Altitude/Construction
ABD = 180 - (ADB + BAC)
CBD = 180 - (CDB + BCA)
A triangle must be 180 degrees
(Algebraically Simplified, using known angles)
90 - BAC
90 - BCA
Simplified
90 - BAC != 90 - BCA
(Note: This is because BAC and BCA are given as NOT EQUAL)
Thus
ABD != CBD
For the angle to bisect ABD must = CBD
But it can't! Thus
BD Does not bisect ABC Because the created angles are not equal.
Def. Bisect
Not knowing your math teacher I dont know how he/she wants these explained, but there is my proof i just made up. :s
