Question

Let A, B, and C be three collinear points s.t. A*B*C. Prove each of the follow set equalities. I'm really having trouble applying theorems like the ruler placement postulate or betweenness theorem to help prove these.

24. Let A, B, and C be three collinear points such that A * B * C. Prove each of the following set equalities. (a) BÁ U BỎ "АС (b) BA n BC {B} (c) ABU BC AC (d) AB n BC {B} (e) AB - AC

Answer 1

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Date BA BC al Solution A, B, C are collinear points i.c lying the same straight line BAUBE From the figure The BÃ l the ray . Be both are in appasite direction and make the line haveing a common endpoint B С C ray So BA UBC AC b) BÀO BC Now these I oppasite rays have only one Common endpoint ie B So, their intersection will give this end point BÁNBC' = {B). Scanned by TapScanner

Date AB U BC A and B Now AB is the segment with end points 47 is a point of the line segment. A toc Ako BĆ ó also a line segment with end point Bbc so, this union BURC AC as AB UAC LAC one So adds ABD RC = {B} The line segment AB LBC have only Endpoint in common ic B AB OC = {B} AB = Ã May Ac is the extended say AB to the point as a ray is extendable Forever in one direction. But both the lays start from the same common Starting point A. scelte So both rays Ão and Al are equal es The Scanned by TapScanner