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 Plane Geometry: For the Use of Schools - Page 71by Nicholas Tillinghast - 1844 - 96 pagesFull view - About this book
| Edith Long, William Charles Brenke - Geometry, Plane - 1916 - 292 pages
...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
...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
...parallel to one of 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
...a square equivalent 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',... | |
| Encyclopedias and dictionaries - 1920 - 934 pages
...parallel to one of 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,... | |
| Edinburgh Mathematical Society - Electronic journals - 1920 - 460 pages
...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... | |
| Robert Remington Goff - 1922 - 136 pages
...330. Two triangles with equal altitudes are to each other as their bases. *331. Two triangles, having **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. *332. Two similar triangles... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...squares. [The solution is 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 an4 A'B'C',... | |
| Edson Homer Taylor, Fiske Allen - Mathematics - 1923 - 104 pages
...right triangles having an acute angle of the one equal to an acute angle of the other. 3. They have one **angle of the one equal to an angle of the other and the** including sides proportional. 4. The three sides of one are proportional to the three sides of the... | |
| Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...similar, if: 1. They have two angles of one respectively equal to two angles of the other. 2. They **have an angle of the one equal to an angle of the other and the** including sides proportional. 3. The sides of one are respectively proportional to the sides of the... | |
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