...by the segments of the other. 4. To inscribe a circle in a given triangle. 5- Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 6. Find the continued product of...

...; Therefore ABC is equiangular to 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'...

...joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the...

...committee suggest that the following proposition be adopted : — If two triangles (or parallelograms) have one angle of the one equal to one angle of the other, their areas are proportional to the areas of the rectangles contained by the sides about the equal...

...therefore, the ratio of DB : BG is compounded of the ratios AB : BE and CB : BF. COR. i. Triangles which have one angle of the one equal to one angle of the other, are to one another in the ratio compounded of the ratios of the sides containing that angle. COR. 2....

...committee suggest that the following proposition be adopted :— If two triangles (or parallelograms) have one angle of the one equal to one angle of the other, their areas are proportional to the areas of the rectangles contained by the sides about the equal...

...area of the polygon on AC is equal to the area of the polygon on BC. EXAMPLES. 1. If two triangles have one angle of the one equal to one angle of the other, and likewise one angle of the one supplementary to one angle of the other, the sides opposite to these...

...describe a square that shall be equal to a given rectilineal figure. 4. 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 conversely. 5. If two chords...

...cent. per annum ? 10. Extract the square root of 3312400. VOLUNTARY PORTION. 1. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. If the sides above mentioned are...

...another case in which two triangles are equal in all respects. PROPOSITION E. THEOREM. If tico triangles have one angle of the one equal to one angle of the otlier, and the sides about a second angle in each equal; then, if the third angles in each be both...