Given magnitudes w, x, y, z, Euclid defines w: x

Elementary Geometry for College Students
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Chapter5: Similar Triangles
Section5.6: Segments Divided Proportionally
Problem 29E: Given point D in the interior of RST, suppose that RG=3,GS=4,SH=4,HT=5, and KT=3. Find RK.
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Given magnitudes w, x, y, z, Euclid defines w: x <y: z as: there are natural numbers m
and n such that mw < nx but my ≥ nz.
(a) Show, with this definition, that 2:3 <3 : 4.
(b) Show that the relation '<' is transitive, which means:
a: b<c:d and c:d<e: f⇒ a: b<e: f.
Transcribed Image Text:Given magnitudes w, x, y, z, Euclid defines w: x <y: z as: there are natural numbers m and n such that mw < nx but my ≥ nz. (a) Show, with this definition, that 2:3 <3 : 4. (b) Show that the relation '<' is transitive, which means: a: b<c:d and c:d<e: f⇒ a: b<e: f.
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