MAT299 Chapter Notes - Chapter 3: Angle, Line Segment, Right Angle

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If a is congruent to b, then b is congruent to a. Euclidean fifth axiom they must intersect each other at one point (if extended infinitely: case 3, suppose two lines intersect each other at 2 or more points. But there could only be 1 unique line between 2 points. 2: note that the area of larger square with side of (b+c) is the sum of the areas of square with side of a and 4 right angle triangles (b+c) =a +4 (b c/2) It is visually clear that ab is the sum of ac and cb i. e. ab=ac+cb: case 2, point c does not lie on line segment ab. In conclusion, ac+cb ab (q. e. d: 2 angles that are complementary to a third angle are congruent. In other words, in isosceles triangle abc, abo = aco. Alternatively, it states that for isosceles triangle abc, ab = ac.

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