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" If two triangles have an angle of one equal to an angle of the other... "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 172
by Euclid, Rev. John Allen - 1822 - 494 pages
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PLANE AND SOLID GEOMETRY

FLETCHER DURELL. PH.D. - 1911
...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...
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Catalogue ...

Yale University. Sheffield Scientific School - 1905
...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 to be the locus of...
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School Science and Mathematics, Volume 22

Education - 1922
...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...
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Plane Geometry Suggestive Method

George Clinton Shutts - 1905
...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...
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The Elements of Geometry

Walter Nelson Bush, John Bernard Clarke - Geometry - 1905 - 355 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...
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Bulletin, Issue 3

Association of Teachers of Mathematics in the Middle States and Maryland - Mathematics - 1906
...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, the square of the...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 254 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...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 418 pages
...by the previous theorems. 198 PROPOSITION VII. THEOREM 414 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. HYPOTHESIS. The & ABC and ADE have the ZA...
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PLANE AND SOLID GEOMETRY

ISAAC NEWTON FAILOR - 1906
...computed by the previous theorems. PROPOSITION VII. THEOREM 414 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. HYPOTHESIS. The & ABC and ADE have the /....
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Exercises in Concrete Geometry: With Supplementary Discussions

David Sands Wright - Geometry - 1906 - 84 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....
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