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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...
SYLLABUS OF PLANE GEOMETRY - Side 17
1876
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## Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 sider
...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 Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 sider
...A'B'C' is similar to the A ABC. QED EXERCISE. 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 AS ABC, A'B'C', let AB AC nv...
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## The Common Sense of the Exact Sciences

William Kingdon Clifford - 1891 - 271 sider
...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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## Elementary Geometry

William Chauvenet - 1893
...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...
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## Examination Papers for the Academic Year ...

1893
...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...
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## Euclid's Elements of Geometry, Bøker 1-6

Henry Martyn Taylor - 1893 - 504 sider
...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 - 1894 - 138 sider
...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...
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## Euclid's Elements of Geometry, Bøker 1-6;Bok 11

Henry Martyn Taylor - 1895 - 657 sider
...ratios AB to DE and BC to EF. Wherefore, if two triangles &c. COROLLARY. If two parallelograms have an angle of the one equal to an angle of the other, the ratio of the areas of th« parallelograms is equal to the ratio compounded of the ratios of the sides...
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## Elements of Geometry: Plane and Solid

John Macnie - 1895 - 374 sider
...angle B, and angle B to angle C, then the figure is a parallelogram. 73. If two parallelograms have an angle of the one equal to an angle of the other, they are mutually equiangular. 74. A parallelogram whose diagonals are equal is a rectangle. 75. A...
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## Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 161 sider
...whatever direction the chord is drawn. 6. Prove the ratio between the areas of two triangles which have an angle of the one equal to an angle of the other. Define area. 7. Define a regular polygon and prove that two regular polygons of the same number of...
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