The Public School Euclid and Algebra . r (h) How does z. GBC compare in magnitude with z. DEFi 3. Show that two isosceles triangles cannot stand on the same base aad on the same side of it, unless the vertex of the one triangle fallsinside the other triangle. 4, Two triangles have the three sides of the one respectively equal to the three sides of the other. Can thev be made to coincide ? 99 EUCLID S ELEMENTS. PROPOSITION 7. Theokkm. 2(A)o triangles on the same hase and on the sai)ie side of it cannotJiave their conterminous sides If it is possible let the two As ABC^ ABD on the same b
The Public School Euclid and Algebra . r (h) How does z. GBC compare in magnitude with z. DEFi 3. Show that two isosceles triangles cannot stand on the same base aad on the same side of it, unless the vertex of the one triangle fallsinside the other triangle. 4, Two triangles have the three sides of the one respectively equal to the three sides of the other. Can thev be made to coincide ? 99 EUCLID S ELEMENTS. PROPOSITION 7. Theokkm. 2(A)o triangles on the same hase and on the sai)ie side of it cannotJiave their conterminous sides If it is possible let the two As ABC^ ABD on the same baseAB, and on the same side of it, have ^IC equal to AD, and BCequal to BD. Three cases may occur : (1) The vertex of each A may be outside the other A- (2) The vertex of one A may be inside the other A . (3) The vertex of one A may be on a side of the other the first case join CD ; and in the second case join CD and produce AC and AD to E and F. Because AC = AD,.-. Z ECD = Z Z ECD is greater than Z Z FDC is greater than Z more then is Z BDC greater than Z because BC* = BD,.. Z BDC = Z BCD ; Pro}). 5. that is, Z BDC is greater than and equal to Z BCD,which is third case needs no proof, because BC is not equal toBD. Hence two triangles on the same base and on the sameside of it cannot have their conterminous sides equal. Prop. 9. EUCLins ELEMENTS. 23 PROPOSITTON H. Thkomkm,If two irviityles have tn)0 sidea of the one equal to tin> siil/>s ofthe othe7\ each to each, an
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