 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 65by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
 | David Eugene Smith - Geometry - 1911 - 360 pages
...tape, is given on page 99. THE TEACHING OF GEOMETRY THEOREM. 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. This proposition may be... | |
 | 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 :... | |
 | Education - 1913 - 396 pages
...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
...in. 31. 13 sq. ft, 9 ft., 5 ft. PROPOSITION VII. THEOREM 332. 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. •A. DB Given the triangles... | |
 | Trinity College (Dublin, Ireland) - 1913 - 568 pages
...equal either to the angle AGP or to the angle ACQ. 7. Prove that if two triangles have an angle of one equal to an angle of the other, and the sides about these equal angles proportional, they are similar. 8. Prove that similar polygons can he divided up... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...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... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...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
...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 - 250 pages
...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. Given FIG. 186. the A ABC and A'B'C', with AB = AC A'C'' and A'B'... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...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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