Using a coordinate geometry approach, identify the coordinates of the vertex of the angle and the equations of the lines forming the two sides; choose an arbitrary point on each line and find the general equation of the line connecting them (the third side of your triangle); write the equation of the line that meets the conditions of angle bisection (that it is equidistant from each of the lines forming the two sides); solve simultaneously the equations for this line and for the third side.
If you are trying to do this as an absolute proof for any angle and triangle, your equations will be full of unknowns (x1, y1, m1, etc), and will need a lot of careful algebraic manipulation. If you have a specific triangle in mind, the presence of numbers makes the solution of the equations much simpler.
Of course, this is not the only method of proof available, but it is the simplest to describe as a general procedure without actually writing out the required proof!
<span>More intuitively, since the angle bisector must be midway between the two rays that form the adjacent sides of the triangle, it must cross any line which intersects those two rays, which the third side of the triangle must do. This is very hard to show as a proof without using diagrams.</span>
Answer:
y = 3/11(x) - 19/11
Step-by-step explanation:
Step 1: Subtract 3x from both sides.
Step 2: Divide both sides by -11.
Therefore, the answer is y = 3/11(x) - 19/11.
Set up a proportion, cross multiply, and solve.
3(7.2) = 4(x)
21.6 = 4x
5.4 = x
This is an example of systems of equations, using weird symbols rather than x or y.
We'll substitute the symbols for the variables d and c
d for diamond, c for clover.
3 + d = c
c + d = 11
We can solve for one variable in the first equation to find the true value of the other variable in the second equation.
3 + d = c
<em><u>Subtract 3 from both sides.</u></em>
d = c - 3
Now we have a value for d and can solve the second equation.
c + d = 11
<em><u>Substitute.</u></em>
c + c - 3 = 11
<em><u>Add 3 to both sides.</u></em>
c + c = 14
<em><u>Combine like terms.</u></em>
2c = 14
<em><u>Divide both sides by 2.</u></em>
c = 7
Now we know the absolute value of c and can solve for the value of d.
d + c = 11
d + 7 = 11
<u><em>Subtract 7 from both sides.</em></u>
d = 4
The diamond, or d, is equal to 4. And the clover, or c, is equal to 7. (This is your answer.)
Let me know if you have any questions.
Answer:
c
Step-by-step explanation:
