| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...they are equal. In the same manner it may be shewn, that B is equal to E, and C to F. PROPOSITION XII. **THEOREM. In an isosceles triangle, the angles opposite the equal sides are equal. LET the side** AB be equal to AC, the angle C will be equal to B. Join A the vertex, and D the middle point of the... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...respectively eqnnl to those of another, the other sides and angle are also equal in the two triangles. 55. **Theorem. In an isosceles triangle the angles opposite the equal sides are equal.** Equal Angles of the Isosceles Triangle. Demonstration. In the isosceles triangle ABC (fig. 32), let... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...at C, and DF be equal to AC, EF equal to BC, and the angle at F equal to the angle at C. PROP. VI. **THEOREM. In an isosceles triangle, the angles opposite the equal sides are equal.** Fig. 6. Let AB, BC, be the equal ! sides ; then we have to prove that the angle A is equal to / i C.... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...equal to BC, and the angle at F equal to the angle atC. ' / // / PROP. VI. THEOREM. ./H^'-i-- , &?• **In an isosceles triangle, the angles opposite the equal sides are equal.** Fig. 6. Let AB, BC, be the equal sides ; then we have to prove that the angle A is equal to C. CDA... | |
| Benjamin Peirce - Geometry - 1847 - 150 pages
...respectively equal to those of another, the other sides and angle are also equal in the two triangles. 55. **Theorem. In an isosceles triangle the angles opposite the equal sides are equal.** Proof. In the isosceles triangle ABC (fig. 32), let the equal sides be AB and BC. Equal Angles of the... | |
| Charles Davies - Trigonometry - 1849 - 384 pages
...observed that the equal angles lie opposite the equal sides: thus, the equal angles D and A, lie op posite **the equal sides EF and BC. • PROPOSITION XI. THEOREM....triangle, the angles opposite the equal sides are equal.** For, join the vertex A, and D the middle point of the base BC. Then, the triangles BAD, DAC, will have... | |
| American Association for the Advancement of Science - Science - 1855 - 396 pages
...the observer at 0', then O' M = his latitude, and PM = 90° ; therefore P D' = • J (90° + lat.). **In an isosceles triangle the angles opposite the equal sides are equal** ; therefore the angle DPC = DOC, but DOC is the azimuth of the object ; therefore the hour-angle of... | |
| Charles Davies - Geometry - 1850 - 218 pages
...coincide with the parts of the triangle DEF, and therefore, the two triangles are equal, THEOREM VI. **In an isosceles triangle the angles opposite the equal sides are equal** to each other, C Let ABC be an isosceles triangle, having the side AC equal to the side CB : then will... | |
| Charles Davies - Geometry - 1850 - 236 pages
...coincide with the parts of the triangle DEF, and therefore, the two triangles are equal. THEOREM VI. **•In an isosceles triangle the angles opposite the equal sides are equal** to each other, Let ABC be an isosceles triangle, having the side AC equal to the side CB : then will... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...angles lie opposite the equal sides, and consequently, the equal sides opposite the equal angles : **thus, the equal angles D and A, lie opposite the equal...the angles opposite the equal sides are equal. Let** BAC be an isosceles triangle, having the side BA equal to the side A0\ then will the angle 0 be equal... | |
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