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. The Essentials of Geometry - Page 170by Webster Wells - 1899 - 395 pagesFull view - About this book
| Rev. John Allen - Astronomy - 1822 - 508 pages
...and of CB to BL oy HE. Cor. 1.—By a similar reasoning it may be proved, that triangles, which have **an angle of one, equal to an angle of the other, are to each other,** in a ratio, compounded of the ratios, of the sides including the equal angles, Cor. 2.—A right line... | |
| Peter Nicholson - Architecture - 1823 - 210 pages
...the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. Two triangles, which have an angle of the **one equal to an angle of the other, are to each other as the** rectangle of the sides about the equal Suppose* the two triangles joined, so as to have a common angle,... | |
| George Clinton Whitlock - Mathematics - 1848 - 336 pages
...(147) with (148).] Of PROPOSITION III. Two triangles, having an angle of the one equal to an (159) **angle of the other, are to each other as the products of the sides** about the equal angles. Let the equal apgles of the triangles A, B, be made vertical, and join the... | |
| Peter Nicholson - Cabinetwork - 1856 - 518 pages
...two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which have an angle of the **one equal to an angle of the other, are to each other as the** rectangle of the sides about the equal angles. Suppose the two triangles joined, so as to have a common... | |
| E. M. Reynolds - Geometry - 1868 - 172 pages
...A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one **angle of the other, are to each other as the products of the sides** containing the equal angle. Let the triangles ABC, A'BC' have equal angles at B. Then shall ABC : A'BC'... | |
| Trinity College (Hartford, Conn.) - 1870 - 1010 pages
...have equal bases and equal altitudes are equal. G. Prove that two triangles which have an angle of the **one equal to an angle of the other are to each other as the** rectangles of the including sides. ENGLISH. I. Correct, criticize, and recast the following sentences:... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of **an angle of the other are to each other as the products of the sides including the** supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described upon the sum of... | |
| William Chauvenet - Geometry - 1871 - 382 pages
...THEOREM. , -•. ,." 57. Two tetraedrons which have a triedral angle of the one equal to a triedral **angle of the other, are to each other as the products of the** three edges of the equal triedral angles. Let ABCD, AB'C'D', be the given tetraedrons, placed with... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of **an angle of the other are to each other as the products of the sides including the** supplementary angles. (IV. 22. ) 220. Prove, geometrically, that the square described upon the sum... | |
| William Chauvenet - Mathematics - 1872 - 382 pages
...PROPOSITION XX.—THEOREM. 57. Two tetraedrons which have a triedral angle of the one equal to a triedral **angle of the other, are to each other as the products of the** three edges of the equal triedral angles. Let AB CD, AB'C'D', be the given tetraedrons, placed with... | |
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