In step 4 the proof contains the error if the AB and BC are perpendicular to each other the option (C) step 4 is correct.
What is the slope?
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two line segments:
AB and BC
AB and BC are perpendicular to each other
AB ⊥ BC
As we know the slope formula:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
After finding the slope draw a vertical line through AC.
As the AB and BC are perpendicular to each other,
Angle ABC is a right-angle triangle.
As we know, the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides is known as, the Pythagoras theorem.
Thus, in step 4 the proof contains the error if the AB and BC are perpendicular to each other the option (C) step 4 is correct.
Learn more about the slope here:
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