(1 point) Instructions: When entering a number in a blank below, always use a nu
ID: 2263750 • Letter: #
Question
(1 point) Instructions: When entering a number in a blank below, always use a numeral. For instance enter "4" instead of writing "four". When referencing Axiom 1 write "a1", etc. A three-point geometry is an incidence geometry that satisfies the following additional axiom: "There exists three points." (a) Let dots represent points and lines (curvey or otherwise) represent lines. Which of the following picutres (you must click on them to see the image accurately) are models for three point geometry (enter "Y" for yes and "N" for no): (b) Prove the following theorem by filling in the blanks. THEOREM: All models for three-point geometry have exactly 3 lines. PROOF If there are 3 points, there are the existence part of Axiom pairs of points. Therefore, every model for three-point geometry has at least lines by the uniqueness part of Axiom Theretore alil moels tor tnree point geometry have exachy linesExplanation / Answer
Every model of three-point geometry has 3 lines.As there are three points in the three-point geometry so there has to be 3 lines to satisfy the incidence Axiom 1 which says that every pair of distinct points defines a unique line.
fill in the blanks:1) there are 2 pairs of points.
2) has atleast 3 lines
3) Axiom 1
4) axiom 1
5) exactly 3 lines
All the given figures do not satusfy these condition , hence none of them have three-point geometry.
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