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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.
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 216
των William Chauvenet - 1872 - 368 σελίδες
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## Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - 1848 - 324 σελίδες
...(147) with (148).] Of PROPOSITION III. Two triangles, having an angle of the one equal to an (159) angle of the other, are to each other as the products of the sides about the equal angles. Let the equal apgles of the triangles A, B, be made vertical, and join...

## Modern Methods in Elementary Geometry by E. M. Reynolds

Edward Morris Reynolds - 1868 - 136 σελίδες
...A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC' have equal angles at B. Then shall ABC...

## Catalogue of the Officers and Students

...similar when they are mutually equiangular. 4. 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. 5. What is the length of the side of a regular decagon inscribed...

## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...whose common vertex will be the point taken within it. ^ VV * PROPOSITION XX.— THEOREM. , -•. ,." 57. Two tetraedrons which have a triedral angle of...D', let fall DO and D'O' perpendicular to the face ABC. Then, taking the faces ABC, AB'C', as the bases of the triangular pyramids D-ABC, D'-AB'C', and...

## A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described...

## Mensuration of lines, surfaces, and volumes

David Munn - 1873
...area of any polygon 43 EXERCISES (4) 44 VIII. 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 47 IX. The areas of similar triangles are to each other as the squares...

## Report, Τόμοι 11-20

1876
...similar when they are mutually equiangular. 2. 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. 3. To inscribe A circle in a given triangle. 4. The side of a regular...

## An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - 1877 - 240 σελίδες
...the other, and the faces including these angles are respectively similar. 112. Two tetraedrons having a triedral angle of the one equal to a triedral angle...the other are to each other as the products of the edges of the equal triedral angles. (70 ; II. 116, 55.) 113. State and prove the converse of Theorem...

## Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...PROPOSITION XIX. THEOREM. 577. Two tetrahedrons having a trihedral angle of the one equal to a trihedral angle of the other are to each other as the products of the three edges of these trihedral angles. Let V and V denote the volumes oî the two tetrahedrons D-ABC, D'-AB'C', having...

## Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 σελίδες
...value. Ex. 1. Show that two triangles which have an angle of the one equal to the supplement of the angle of the other are to each other as the products of the sides including the supplementary angles. С \j 2. Show, geometrically, that the square described upon...