| 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 - 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... | |
| 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 :... | |
| 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, 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... | |
| 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... | |
| Encyclopedias and dictionaries - 1920 - 934 pages
...its sides. Triangles which have their homologous sides proportional are similar. Two triangles which **have an angle of the one equal to an angle of the other, and the sides** about these angles proportional, are similar. Two triangles which have their sides parallel or perpendicular,... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...to the sum of three given squares. 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',... | |
| Edinburgh Mathematical Society - Electronic journals - 1920 - 460 pages
...are collinear. The theorem in similarity corresponding to the converse theorem (2) is the following : **If two triangles have an angle of the one equal to an angle of the other and** another pair of angles supplementary, then the sides opposite to the equal angles are proportional... | |
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