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" If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 35
by Benjamin Greenleaf - 1862 - 490 pages
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, since if FE were produced toward H, the angles DEH,...THEOREM. 94. If any side of a triangle be produced, the exteriorangle is equal to the sum of the two interior and. opposite angles. Let ABC be a triangle,...
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Study of Steam and the Marine Engine for Young Sea Officers in H.M. Navy ...

S. M. Saxby - Marine engines - 1862 - 200 pages
...double of ECB, so must the whole angle ADB be the double of the angle AC B. *28. Euc. I. Prop. XXXII.— If any side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of any triangle are equal to two right...
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, since if FE were produced toward H, the angles DEH,...angle is equal to the sum of the two interior and opposite angles. Lot ABC bo a triangle, and lot one of its sides, BC be produced towards D ; then the...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...the side EF lies in the same direction with BC, since if FE were produced toward H, the angles DE H", ABC would only be equal when they are right angles....angle is equal to the sum of the two interior and opposite angles. Let ABC be a triangle, and AE lot one of its sides, BC be pro- /\ duced towards D...
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Half-hour examination papers, for daily use

John Robertson (LL.D., of Upton Park sch.) - Examinations - 1865 - 144 pages
...in the same, and thence show that two straight lines cannot have a common segment. [ECS] 43. If the side of a triangle be produced, the exterior angle is equal to the two interior opposite angles : and the three interior angles of every triangle are together equal to...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865
...is one-third of two right angles, or two thirds of one right angle. PROPOSITION XXXI. THEOR. If one side of a triangle be produced, the exterior angle is equal to the two interior opposite angles. Let BC, one of the sides of the triangle ABC, be produced to D, the exterior...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Conic sections - 1865 - 472 pages
...angles. Hence the theorem ; the sum of the three angles, etc. THEOREM XII. If any side of a triangle is produced, the exterior angle is equal to the sum of the two interior opposite angles. Let ABC be a triangle. Produce AB to D; and we are to prove that the angle CBD is...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1866 - 328 pages
...the case where the side EF lies in the same direction with BC, since if FE were produced toward II, the angles DEH, ABC would only be equal when they...angle is equal to the sum of the two interior and opposite angles. Let ABC be a triangle, and let one of its sides, BC be produced towards D ; then the...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 338 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, since if FE were produced toward H, the angles DEH,...side of a triangle be produced, the exterior angle ii equal to the sum of the two interior and ojipositu angles. Let ABC be a triangle, and let one of...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...Scholium. This proposition is restricted to the case where the side EF lies in the same direction with BC, since if FE were produced toward H, the angles DEH,...only be equal when they are right angles. PROPOSITION XX VII. r— THEOREM. 94. If any side of a triangle be produced, the exterior angle is equal lo the...
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