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" The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... "
Elements of Geometry - Page 65
by Adrien Marie Legendre - 1841 - 235 pages
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 208 pages
...altitudes, both when the latter are commensurable and incommensurable. 4. The areas of two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. 5. Given a square the length...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...equal, respectively, to two angles of the other. PROPOSITION XVIII. THEOREM. 357. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are sintilar. In the triangles ABC and A'B'C', let ^ A = Z A', and...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...to half the sum of its bases multiplied by the altitude. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. 412. The areas of two similar...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...other vertices of the polygon. D PROPOSITION VII. THEOREM. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Let the triangles ABC and...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...vertices of the polygon. PROPOSITION VII. THEOREM. ).-•. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other us the products of the sides including the equal angles. Let the triangles ABC and...
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Preparatory Schools for Boys: Their Place in English Secondary Education

Great Britain. Board of Education - Boys - 1900 - 531 pages
...as CD. The diagonals AC, BD intersect at 0. Show that CO is a quarter of С A. V. Two triangles have an angle of the one equal to an angle of the other, and the sides about those angles proportionals. Prove the triangles similar. VI. AB is a tangent to a circle and A CD is...
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Sessional Papers, Volume 22, Part 2

Great Britain. Parliament. House of Commons - Great Britain - 1900
...CD. The diagonals AC, Bl) intersect at 0. Show that (70 is a quarter of CA . V. Two triangles have an angle of the one equal to an angle of the other, and the sides about those angles proportionals. Prove the triangles similar. VI. AB is a tangent to a circle and ACD is...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

Education - 1901
...to a given straight line ; if A(f he bisected in fí, find the locus of R. 6. If two triangles have an angle of the one equal to an angle .of the other, and the sides about the equal angles proportionals, the triangles shall he similar. 13_ In the side ЛГ> of the triangle AUC a point I>...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...given circle an equilateral and equiangular hexagon. 10. Two obtuse.angled triangles have one acute angle of the one equal to an angle of the other, and the sides about the other acute angle in each proportionals ; prove that the triangles are similar. 11. Prove that if four...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 440 pages
...triangle is equal to half the product of its base and altitude. § 306. (6) The areas of two triangles having an angle of the one equal to an angle of the other are in the same ratio as the products of the sides containing the equal angles. § 308. 6. THEOREMS...
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