A Geometry for Beginners
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In our eReader you can find the full English version of the book. Read A Geometry for Beginners Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Geometry for Beginners
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To quickly assess the difficulty of the text, read a short excerpt:
149. Problem. To transform a rectangle ABCD (Fig. 138) into a square.
Construction. Make BE = BC, and about O, the middle point of B E, describe an arc cutting DA prolonged in F. Join FB, and the square con- structed upon FB will be equal in area to the rectangle ABCD.
Proof. EBF is a right triangle. For the triangles OEF and OBF are isosceles (why?) ; hence EFO = FEO, and OFB = OBF ( 80). By addi- tion, EFO + OFB = EFB = FEO -f OBF. But EFB + FEO + OBF = 180 ( 64) ; therefore EFB = 90.
l&L.
Fi...g. 138.
Since EBFis a right triangle, it follows from 142, Corollary 3, that ~FJ? = the area of the rectangle ABCD.
Exercises. 1. Construct a rectangle with the sides 9 dm and 4 dm, and transform it into a square. Measure the side of the square. What is its length ? What ought its length to be ?
2. Construct a triangle with the sides 4 dm, 6 dm, and 8 dm, and transform it into a square.
3. Transform a given parallelogram into a square.
150. Problem. To transform any polygon ABCDE (Fig. 139} int a triangle.
What to read after A Geometry for Beginners?
You can find similar books in the "Read Also" column, or choose other free books by George Anthony Hill to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
149. Problem. To transform a rectangle ABCD (Fig. 138) into a square.
Construction. Make BE = BC, and about O, the middle point of B E, describe an arc cutting DA prolonged in F. Join FB, and the square con- structed upon FB will be equal in area to the rectangle ABCD.
Proof. EBF is a right triangle. For the triangles OEF and OBF are isosceles (why?) ; hence EFO = FEO, and OFB = OBF ( 80). By addi- tion, EFO + OFB = EFB = FEO -f OBF. But EFB + FEO + OBF = 180 ( 64) ; therefore EFB = 90.
l&L.
Fi...g. 138.
Since EBFis a right triangle, it follows from 142, Corollary 3, that ~FJ? = the area of the rectangle ABCD.
Exercises. 1. Construct a rectangle with the sides 9 dm and 4 dm, and transform it into a square. Measure the side of the square. What is its length ? What ought its length to be ?
2. Construct a triangle with the sides 4 dm, 6 dm, and 8 dm, and transform it into a square.
3. Transform a given parallelogram into a square.
150. Problem. To transform any polygon ABCDE (Fig. 139} int a triangle.
What to read after A Geometry for Beginners?
You can find similar books in the "Read Also" column, or choose other free books by George Anthony Hill to read onlineMoreLess
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