Books Books Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides... Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 94
by Dennis M'Curdy - 1846 - 138 pages ## Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 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... ## Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...8. (/or its equal A AFH is similar to A ABC). QED PROPOSITION XVII. THEOREM 327. 7/ jfwo triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. A Given the A ABC and A'B'C', in which... ## Catalogue ...

Yale University. Sheffield Scientific School - 1905 - 1074 pages
...hypotenuse of a similar triangle is 1o in. What is the area of the second triangle? 6. The areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including the equal angles. 7. When is a circle said... ## School Science and Mathematics, Volume 22

Education - 1922 - 948 pages
...and C; draw OD J.AC; since <B = <AOD, \ve may apply to AsABC and AOD the theorem: If two triangles have an angle of one equal to an angle of the other, the ratio of their areas equals the ratio of the products of the sides including this angle. Hence... ## The Elements of Geometry

Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 378 pages
...proportional between their diameters. XVI. GROUP ON AREAL RATIOS PROPOSITIONS XVI. 1. If two triangles have an angle of one equal to an angle of the other, they are to each other as the rectangles of the sides respectively including the equal angles. A c... ## Plane Geometry Suggestive Method

George Clinton Shutts - 1905 - 260 pages
...circumferences are parallel. Prove AD parallel to B C. PROPOSITION XIX. 303. Theorem. // two triangles have an angle of one equal to an angle of the other, and the sides including the equal angles proportional, the triangles are similar. A A' In the triangles... ## Exercises in Concrete Geometry: With Supplementary Discussions

David Sands Wright - Geometry - 1906 - 104 pages
...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.... ## Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 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. BCE r Given : A ABC and... ## Bulletin, Issue 3

...straight angle. (Necessary to prove propositions concerning concurrent lines.) *P16. Triangles that have an angle of one equal to an angle of the other, are to each other as the products of the sides containing those angles. *P18. In any obtuse triangle,... 