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" If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. "
The first six books of the Elements of Euclid, with numerous exercises - Seite 13
von Euclides - 1853 - 147 Seiten
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878 - 209 Seiten
...angles is equal to R. COR. 5. In an equiangular triangle, each angle is equal to ^ of 2R = | R. XVIII. Theorem. If one side of a triangle be produced, the exterior angle is equal to the two interior angles not adjacent. HYPOTH. In the triangle ABC, one side, AB, is produced,...
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Elements of Plane Geometry, Teil 1

Thomas Hunter - 1878 - 132 Seiten
...angles AFB and DAF are equal, the lines DE and BC are parallel (Prop. XXV.). PROPOSITION XXX.—THEOREM. If one side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles, and the three angles of the triangle are...
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Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

James Hamblin Smith - 1879 - 349 Seiten
...line, and QP a line which revolves about the fixed point Q, and which at first coincides with QE. 7F PROPOSITION XVI. THEOREM. If one side of a triangle...greater than either of the interior opposite angles. -JSS Let the side BC of AA JRC be produced to D. Then must L ACD be greater than either i CAB or L...
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A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 Seiten
...in all respects. Same proposition. Give corollaries. • Propositions XVI. -XXVI. (inclusive). 16. If one side of a triangle be produced, the exterior...greater than either of the interior opposite angles. • Same proposition. Show that only one perpendicular can be drawn from a given point to a given straight...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 Seiten
...angles made by any number of lines meeting in a point, are equal to four right angles. Proposition 18. Theorem. — If one side of a triangle be produced, the exterior angle is greater than either of the opposite interior angles. Let the side BC of the triangle ABC be produced to D; then will A CD be greater...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...unlimited length. (5) Prove that any two angles of a triangle are together less than two right angles. (6) If one side of a triangle be produced, the exterior angle is greater than either of the interior and opposite angles. Show that only one perpendicular can be drawn from a given point to a given straight...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...CAREFULLY SELECTED FROM THE Cambridge Mathematical Tripos Examination Papers (1867-77). Jan. 1867. 1. If one side of a triangle be produced, the exterior angle is greater than either of the two interior opposite angles. Any two exterior angles of a triangle are together greater than two right...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...same side of a given line, draw two lines which shall meet in that line and make equal angles with it. PROPOSITION XVI. THEOREM. If one side of a triangle be produced, the exterior angle shall be greater than either of the interior opposite angles. Let ABC be A, and let any side BC be...
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Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

Euclides, James Hamblin Smith - 1879 - 349 Seiten
...Again, in Prop. xv. it is evident that L AED = L BEC, since each has the same supplementary / AEC. PROPOSITION XVI. THEOREM. If one side of a triangle be produced, the erterior angle ii greater than either of the interior opposite angles. D Let the side BC of A ABC he...
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Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey

Euclid, F. B. Harvey - 1880 - 119 Seiten
...Prove in Prop. XV. that the angle CEB = the angle AED. 2. Prove each of the above Corollaries. PROP. XVI. • THEOREM. If one side of a triangle be produced,...greater than either of the interior opposite angles. Let ABC be a triangle, and let the side BG be produced toD. Then it is to i>e proved that The exterior...
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