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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. Plane Geometry - Page 180by Arthur Schultze - 1901Full view - About this book
| George Albert Wentworth - Geometry - 1877 - 416 pages
...4 ÊF* = AC1 + SD* + 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having **an angle of the one equal to an angle of the other are to each other as the products** cf t he sides including the equal angles. Let the triangles ABC and ADE have the common angle A. We... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...4 = AC? + BI? + 4 ^ QED GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having **an angle of the one equal to an angle of the other are to each other as** tAe products of the sides including the equal angles. D. Let the triangles ABC and ADE have the common... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...value. Ex. 1. Show that two triangles which have an angle of the one equal to the supplement of the **angle of the other are to each other as the products of the sides including the** supplementary angles. С \j 2. Show, geometrically, that the square described upon the sum of two straight... | |
| William Frothingham Bradbury - Geometry - 1877 - 262 pages
...are respectively similar. 112. Two tetraedrons having a triedral angle of the one equal to a triedral **angle of the other are to each other as the products of the** edges of the equal triedral angles. (70 ; II. 116, 55.) 113. State and prove the converse of Theorem... | |
| Elias Loomis - Conic sections - 1877 - 458 pages
...the point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they **have an angle of the one equal to an angle of the other,** and the sides including those angles proportional. Let the triangles ABC, DEF have the angle A of the... | |
| George Albert Wentworth - Geometry - 1877 - 426 pages
...PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the oiher are **to each other as the products of the sides including the equal angles.** Д Let the triangles ABС and ADE have the common angle A. Tjr , АABС ABX AС \\ e are to prove =... | |
| George Albert Wentworth - Geometry - 1877 - 436 pages
...EH AE = B'C'' A'B' B'C' =A'B', Hyp. Ax. 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles having **an angle of the one equal to an angle of the other,** and the including sides proportional, are similar. A A' In. the triangles ABC and A' B' С' let /А... | |
| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...Cor. 3). ABE BE .. . ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. If two triangles **have an angle of the one equal to an angle of the other,** the ratio of their areas is equal to that of the products of the sides which contain those angles.... | |
| James McDowell - 1878 - 310 pages
...DEF are equiangular (constr.), therefore ABC and DEF are also equiangular. QED 81. If two triangles **have an angle of the one equal to an angle of the other,** and the rectangles under the sides about the equal angles equal, a side of each triangle being taken... | |
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