 ... have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.  Plane Geometry - Page 189by Edith Long, William Charles Brenke - 1916 - 276 pagesFull view - About this book
 | Webster Wells - Geometry - 1886 - 392 pages
...Therefore ZA = Z B'A'C'. In like manner it may be proved that ZB = Z A'B'C' . Therefore the triangles have two angles of one equal respectively to two angles of the other, and are similar. 279. SCHOLIUM I. In similar triangles whose sides are respectively perpendicular,... | |
 | George Irving Hopkins - 1891 - 210 pages
...Theorem 314, and the remainder of the demonstration should be easy. QED 348. If two triangles have two angles of one equal respectively to two angles of the other, the two triangles are similar. 349. If two right triangles have an acute angle of one equal to an acute... | |
 | 1894 - 788 pages
...sum of the distances of the third angular point from the same two points. 2. If two triangles have two angles of one equal respectively to two angles of the other, and a side of one equal to a side similarly placed with respect to the equal angles of the other, the... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...including these angles proportional, the triangles are similar. 241. COR. 2. If two triangles have two angles of one equal respectively to two angles of the other, the triangles are similar. 242. COR. 3. If two right triangles have an acute angle of one equal to... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...triangle is greater than either of the opposite interior angles. 86. Cor. II. If two triangles have two angles of one equal respectively to two angles of the other, the third angle of the first is equal to the third angle of the second. 87. Cor. III. A triangle cannot... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...of one are equal, respectively, to the three angles of the other. § 249. (2) If two triangles have two angles of one 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... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...therefore by definition they are similar. QED 479. COROLLARY. Two triangles are stmilar if they have two angles of one equal respectively to two angles of the other. 480. EXERCISE. All equilateral triangles are similar. 482. EXERCISE. If the sides of a triangle ABC... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...ARST. SUG. Apply Theo. XXIV, Cor. 4, and Theo. VII. Conclusion. THEOREM XXVI 74. If two triangles have two angles of one equal respectively to two angles of the other and the sides opposite a pair of equal angles equal, the triangles are equal. Hyp. In the A XYZ and... | |
 | Frederick E. Sears - 1905 - 52 pages
...(having their sides perpendicular each to each.) .•. the triangles ABC and DNP are similar. (having two angles of one equal respectively to two angles of the other.) . •. The homologous sides of the two similar triangles are DN = pull of gravity on W or the weiffht... | |
 | Education - 1913 - 914 pages
...angles of a triangle is two right angles. III. Important dependent theorems. a. If two triangles have two angles of one equal respectively to two angles of the other, the third angles are equal. b. An exterior angle of a triangle equals, etc. c. Theorems for the sum... | |
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