So, according to Euclid's division lemma, If we have two positive integers a and b, then there would be whole numbers q and r that satisfy the equation: a = bq + r, where 0 < r < b . a is the dividend. b is the divisor. q is the quotient and r is the reminder.
If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then other two sides are divided in the same ratio ...this is Thales theorem
1. In number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers, namely: Euclid's lemma — If a prime p divides the product ab of two integers a and b, then p must divide at least one of those integers a and b.
2. The Thales theorem states that: If three points A, B, and C lie on the circumference of a circle, whereby the line AC is the diameter of the circle, then the angle ∠ABC is a right angle (90°).
For a parallel line the slope of the lines/equations will be the same but for perpendicular line the slope will be the negative reciprocal -(1/4)*x+b b=2-(-1/4)*8
