| Arthur Schultze - 1901
...three given squares. PROPOSITION XV. THEOREM 369. 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 a B' A' D' Hyp. In triangles ABC and A'B'C',... | |
| Thomas Franklin Holgate - Geometry - 1901 - 440 pages
...equal, respectively, to two angles of the other, the triangles are similar. § 250. (3) If two triangles **have an angle of one equal to an angle of the other,** and the sides including these angles proportional, the triangles are similar. § 251. (4) If the ratios... | |
| Arthur Schultze - 1901
...three given squares. PROPOSITION XV. THEOREM 369. 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... | |
| George Albert Wentworth - Geometry, Solid - 1902 - 218 pages
...products of their bases by their altitudes. 410. 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. 412. The areas of two similar polygons are... | |
| James McMahon - Geometry, Plane - 1903 - 358 pages
...Similarly, it may be proved that B"C" = B'C'. Two sides and included angle. 44. THEOREM 10. If two triangles **have an angle of one equal to an angle of the other,** and the sides about these angles proportional, then the triangles are similar. Let the triangles ABC... | |
| John Alton Avery - Geometry, Plane - 1903 - 122 pages
...triangle, a smaller triangle is formed similar to the given triangle. THEOREM V 164. If two triangles **have an angle of one equal to an angle of the other,** and the including sides proportional, the triangles are similar. Hyp. In the A RST and R'S'T', let... | |
| American School (Chicago, Ill.) - Engineering - 1903
...A', and ^^_ = — — A. 1 1 ./Y li Therefore the triangles ABE and A' B' E' are similar, for they **have an angle of one equal to an angle of the other,** and the sides including these angles proportional (Theorem LIII). Again, since the polygons are similar,... | |
| Fletcher Durell - Geometry, Solid - 1904 - 206 pages
...326. // two triangles have their homologous sides proportional they are similar. 327. // two triangles **have an angle of one equal to an angle of the other,** and the including sides proportional, the triangles are similar. 328. // two triangles have their sides... | |
| Fletcher Durell - Geometry, Plane - 1904 - 372 pages
...is similar to A ABC). Art. 306. Art. 101. Ax. 8. QED PROPOSITION XVII. THEOREM 327. If two triangles **have an angle of one equal to an angle of the other,** and the including sides proportional, the triangles are similar. Given the A ABC and A'B'C', in which... | |
| George Albert Wentworth - Geometry - 1904 - 473 pages
...AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 410. 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. Let the triangles ABC and ADE have the common... | |
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