 | Charles Scott Venable - 1881 - 380 pages
...contact is a mean proportional between the diameters of the two circles. 30. If two triangles have an angle in one equal to an angle in the other, and a second angle in one supplementary to an angle in the other, the sides of the triangles respectively... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...the other. Therefore the triangles are similar (367). Q- ED Fig. 183. PROPOSITION V. 373. Theorem.— Two triangles having an angle in one equal to an' angle in the other, and the sides about the equal angles proportional, are similar. •' ' > AC DF CB FE' DEMONSTRATION. Let ABC and DEF have... | |
 | Dublin city, univ - 1885 - 476 pages
...triangle expressed in terms of two sides and the included angle ? 4. Prove that two triangles which have an angle in one equal to an angle in the other, and the sides about the equal angles reciprocally proportional, are equal in area. 5. Rationalise the denominator of the... | |
 | Dalhousie University - 1888 - 212 pages
...the lines drawn from Q to all the other angles bisect them. 7. If two triangles have an angle in the one equal to an angle in the other, and the sides about these equal angles proportional, then must the triangles be similar. 8. If two opposite sides of a quadrilateral inscribed in a circle... | |
 | George Clinton Shutts - Geometry - 1912 - 392 pages
...Proof. SUG. Find the ratio of the areas and simplify the expression. PROPOSITION VII. 368. THEOREM. Two triangles having an angle in one equal to an angle in the other are proportional to the products of the sides including the equal angles. Given A EFG and A E'F'G'... | |
 | Queen's University (Kingston, Ont.) - 1913 - 770 pages
...sides, of each point of contact from the adjacent vertices. 10. If two triangles have an angle in the one equal to an angle in the other, and the sides about another pair of corresponding angles proportional, the remaining pair of corresponding angles are either... | |
 | Ernst Rudolph Breslich - Mathematics - 1916 - 392 pages
...triangles having equal bases (altitudes) are to each other as the altitudes (bases). 14. The areas of two triangles having an angle in one equal to an angle in the other are to each other as the products of the sides including the equal angles. I5. The areas of similar... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...altitude as the other given triangle, using another- pair of sides as bases. Proposition IX. Theorem 255. Two triangles, having an angle in one equal to an angle in the other, are to each other as the products of the sides forming the equal angles. Hyp.: Given the triangles... | |
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FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi. 
