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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 - Σελίδα 13
των Euclides - 1853 - 147 σελίδες
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878 - 209 σελίδες
...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,...

Elements of Plane Geometry, Μέρος 1

Thomas Hunter - 1878 - 132 σελίδες
...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...

Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

James Hamblin Smith - 1879 - 349 σελίδες
...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...

A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 σελίδες
...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...

The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 σελίδες
...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...

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...

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...

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...

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879
...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...

Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey

Euclid, F. B. Harvey - 1880 - 119 σελίδες
...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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