The Elements of Plane And Solid Geometry
The Elements of Plane And Solid Geometry
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Proof. Since Z B = / B', (Hyp. ) A ABC BA X BC BA BC ' ' ' ZA'B'C' ~ B'A' X B'C' ~ r B'A' X B'C' ' BA BC B'A'~B'C" Jwmologous sides of similar AS are proportional (307).
Substitute in the above equality for ^r-, its equal ^77 Jt> . A. JD \j A ABC BO B0 BG a _ A A'B'C 7 ~~ WC' X B'C' ~ g 7 ^' 2 ' 378. Cor. The areas of two similar triangles are to each other as the squares of any two homologous lines. EXERCISES.
1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides BC..., AC in E and F. Com- pare the areas of the triangles AGB, FGE.
2. The base and altitude of a triangle are 18 and 8 re- spectively; what is the altitude of a similar triangle whose base is 12 ?
3. A has a triangular piece of ground, the base of the triangle being 40 rods; what is the base of a similarly- shaped lot containing 4 times as much ? Ans. 80 rods.
190 PLANE GEOMETRY.
Proposition 1 0. Theorem.
379. Tlie areas of similar polygons are to each other as tlie squares of their homologous sides.
What to read after The Elements of Plane And Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Edward a Edward Albert Bowser to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Proof. Since Z B = / B', (Hyp. ) A ABC BA X BC BA BC ' ' ' ZA'B'C' ~ B'A' X B'C' ~ r B'A' X B'C' ' BA BC B'A'~B'C" Jwmologous sides of similar AS are proportional (307).
Substitute in the above equality for ^r-, its equal ^77 Jt> . A. JD \j A ABC BO B0 BG a _ A A'B'C 7 ~~ WC' X B'C' ~ g 7 ^' 2 ' 378. Cor. The areas of two similar triangles are to each other as the squares of any two homologous lines. EXERCISES.
1. ABC is a triangle. AE and BF, intersecting in G, are drawn to bisect the sides BC..., AC in E and F. Com- pare the areas of the triangles AGB, FGE.
2. The base and altitude of a triangle are 18 and 8 re- spectively; what is the altitude of a similar triangle whose base is 12 ?
3. A has a triangular piece of ground, the base of the triangle being 40 rods; what is the base of a similarly- shaped lot containing 4 times as much ? Ans. 80 rods.
190 PLANE GEOMETRY.
Proposition 1 0. Theorem.
379. Tlie areas of similar polygons are to each other as tlie squares of their homologous sides.
What to read after The Elements of Plane And Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Edward a Edward Albert Bowser to read onlineMoreLess
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