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" Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. "
The Elements of geometry; or, The first six books, with the eleventh and ... - Page 135
by Euclides - 1855
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 274 pages
...proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. 326. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA=ZA',...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 386 pages
...proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. V 326. If two triangles have an angle of the one equal to an angle of the othcr, and the including sides proportional, they are similar. In the triangles ABC and A'B'C ' , let...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...= 12, and AC — 10, find the lengths of the segments BD and CD. Proposition 1 8. Theorem. 314. Two triangles which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. Hyp. In the A s ABC, A'B'C', let AB AC...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
...their sides about the equal angles reciprocally proportional : (/3) and conversely, if two triangles have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, the triangles have the same area. Let...
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The Common Sense of the Exact Sciences

William Kingdon Clifford - Mathematics - 1891 - 312 pages
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respsctively equal, they must be equal in all particulars. For...
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Examination Papers for the Academic Year ...

Examinations - 1893
...tangent and a chord is measured by one half the intercepted arc. 1 2 5 Prove that the areas of 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. 16 6 Prove that the area of a regular...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...hence AD BC 'AT? A'D' B'C' and we have ARC _ = 'AT? A'B'O' EXERCISE. Theorem. — Two triangles having 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. Suggestion. Let ADE and ABC be...
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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 504 pages
...is to CD as EF to GH. (V. Prop. 16.) Wherefore, if the ratio ,fec. PROPOSITION 23. If two triangles have an angle of the one equal to an angle of the other, tlte ratio of the areas of the triangles is equal to the ratio compounded of the ratios of the sides...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...circumferences at B and C respectively ; show that BA is perpendicular to AC. 4. Assuming that the areas of 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, prove that the bisector of an angle...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 392 pages
...QED (232"') SCHOLIUM. The theorem may be expressed also under the form : The areas of triangles that have an angle of the one equal to an angle of the other, are as the products of the sides about those angles. PROPOSITION IX. THEOREM. 342. Similar triangles are...
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