Elementary plane geometry : inductive and deductive / by Alfred Baker . times as high as the rectangle BCLM(which is equal to the triangle ABC). That is, of suchparts as EF contains 7, BC contains 4; and of suchparts as FN contains 7, CL contains 4. Hence of suchsmall areas as the rectangle EFNP contains 7-=49,the rectangle BCLM contains 4-=16. And thereforethe triangle ABC is to the triangle DEF as 16 is to 49. That is, when BC:EF = 1:13 = 4:7,then, triangle ABC: triangle DEF = 16 : 49 = 4^ : 7^ or l:(lf) 142 Geometky. 3. Make figures as iu § 1 and § 2 for the followingproblems: Two simila
Elementary plane geometry : inductive and deductive / by Alfred Baker . times as high as the rectangle BCLM(which is equal to the triangle ABC). That is, of suchparts as EF contains 7, BC contains 4; and of suchparts as FN contains 7, CL contains 4. Hence of suchsmall areas as the rectangle EFNP contains 7-=49,the rectangle BCLM contains 4-=16. And thereforethe triangle ABC is to the triangle DEF as 16 is to 49. That is, when BC:EF = 1:13 = 4:7,then, triangle ABC: triangle DEF = 16 : 49 = 4^ : 7^ or l:(lf) 142 Geometky. 3. Make figures as iu § 1 and § 2 for the followingproblems: Two similar triangles, ABC and DEF, have their cor-responding sides BC and EF, 1 and 2 inches in lengthrespectively J show that their areas are as 1 to 4, ,as 1 to 22. Two similar triangles, ABC and DEF, have their cor-responding sides BC and EF, 1 and Ih inches in lengthrespectively; show that their areas are as 4 to 9, 1 to {Uy. Two similar triangles, ABC and DEF, have their cor-responding sides BC and EF, 30 and 50 millimetres inlength respectively; show that their areas are as 9 to25, , as (30)2 to (50)2. (For the tliree preceding constructions, the methodof article 4, which follows, should also be employed.) The result of our observations in such cases as thepreceding may be stated thus: Similar triangles are to one another as thesquares of corresponding sides. Note: In the preceding examples it will be ob-served that the lengths of the corresponding sides aresupposed commensurable, ,
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