 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'...  An Elementary Treatise on Plane and Solid Geometry - Page 146by Benjamin Peirce - 1871 - 150 pagesFull view - About this book
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...C'B', Const CA:CP = CB:CQ. Ax. 9 Also ZC = Z C. Iden. .-. A ABC and PQC are similar. § 288 (If two & have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar.) .-.CA:CP = AB:PQ; §282 that is, CA : C'A ' = AB :... | |
 | Education - 1913 - 396 pages
...drawn and only one If two triangles have their homologous sides proportional they are similar If two triangles have an angle of the one equal to an angle of the other their areas are to each other as the products of the sides including the equal angles The area of a... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...• 1 AA'B'C' AW Proof. Since the triangles are similar, Given §282 (The areas of two triangles that 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.) AABC AB AC AC (Similar... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...left to the student.] PLANE GEOMETRY PROPOSITION XIII. THEOREM 378. 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. Given A ABC and A'B'C',... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...Const. CA:CP = CB:CQ. Ax. 9 Also ZC = ZC Iden. .'. A^J5C and PQC are'similar. § 288 (If two A /iaue a?i angle of the one equal to an angle of the other, and the including sides proportional, they are similar.) a '.CA:CP = AB:PQ; §282 that is, CA : C'A' = AB :... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...[The solution is left to the student.] PROPOSITION XIII. THEOREM 378. 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 product of the sides including the equal angles. Given A ABC and A'B'C', Z... | |
 | Queensland. Department of Public Instruction - Education - 1914 - 284 pages
...inscribed in a circle is half that of the square oircumBCribed about the same circle. 8. Prove that if two triangles have an angle of the one equal to an angle of the other arxcl the sides about these angles proportional the triangles will be similar. 9. Two circles intersect... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...equal to an acute angle of the other. PLANE GEOMETRY 410. THEOREM. Two triangles are similar, if they have an angle of the one equal to an angle of the other and the including sides are proportional. , FIG. 186. Given the A ABC and A'B'C', with ZA = Z A', and AB =... | |
 | Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...proportional to their corresponding sides. Suggestion. Apply Art. 220, Cor. 3. 222. Theorem XVI. // two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, the triangles are similar. Given the triangles ABC and AiBiCi with angle... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...proportional to their corresponding sides. Suggestion. Apply Art. 220, Cor. 3. 222. Theorem XVI. // two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, the triangles are similar. Given the triangles ABC and AiBiCi with angle... | |
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