 | David Sands Wright - Geometry - 1906 - 104 pages
...are similar if — 1. They are mutually equiangular. 2. Their homologous sides are proportional. 3. They have an angle of one equal to an angle of the other, and the sides including the equal angles are proportional. 4. The homologous sides are parallel. 5. The homologous... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...to an acute angle of the other. PROPOSITION XVIH. THEOREM 354 If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. HYPOTHESIS. In the triangles ABC and A'B'C', £ A = Z A', and AB : A'B' = AC : A'C'.... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...the including sides proportional. .-. the A OAB and BAC are similar. "If two A have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar." § 354 But the A OAB is isosceles. § 221 /. the A COB is isosceles, and Z 0 = Z... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...other side, the parallelogram formed is equivalent to the trapezoid. 34. If two equivalent triangles have an angle of one equal to an angle of the other, the sides including these angles are reciprocally proportional. 35. The sum of the three perpendiculars... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...AMN = ZB; Z ANM = ZC (?) (98). ... A are similar (?) (313). QED B C 317. THEOREM. 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. D BCE Given : A ABC and DEF;... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...other side, the parallelogram formed is equivalent to the trapezoid. 34. If two equivalent triangles have an angle of one equal to an angle of the other, the sides including these angles are reciprocally proportional. 35. The sum of the three perpendiculars... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...one of the tests of similarity is satisfied. PROP. XV. THEOREM 242. Two triangles are similar when they have an angle of one equal to an angle of the other, and the sides including these angles proportional. Draw A ABC and A'B'C' having ZA = ZA', and the sides including... | |
 | Albert Harry Wheeler - Algebra - 1908 - 698 pages
...are taken parallel to the axis of Y, and accordingly the triangles OfiA and OH' A' are similar, since they have an angle of one equal to an angle of the other, and the included sides proportional. It follows that either of the points A or A' lies on the straight line... | |
 | Webster Wells - Geometry - 1908 - 338 pages
...equal to two angles of the other (§ 236). When their homologous sides are proportional (§ 240). When they have an angle of one equal to an angle of the other, and the sides including these angles proportional (§ 242). When their sides are parallel each to each, or... | |
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... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. 
