| E. J. Brooksmith - Mathematics - 1889
...method of proof must be geometrical. Great importance will be attached to accuracy.] 1 . If a side of a **triangle be produced, the exterior angle is equal to the two interior and opposite angles.** Through the vertices of a triangle ABC straight lines, falling within the triangle, are drawn making... | |
| George William Usill - Surveying - 1889 - 272 pages
...same straight line are parallel to one another. 18. If a side of any triangle B c be produced to D, **the exterior angle is equal to the two interior and opposite angles, and the** IS three interior angles of every triangle are together equal to two right angles. 19. The exterior... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...congruent (I. 8), and have sides AE, DE parallel respectively to BC, AH (I. 27). PROPOSITION 32. THEOREM. **If a side of any triangle be produced, the exterior...triangle are together equal to two right . angles.** Let ABC be a A having one side BC produced to D ; then ext. L ACD = twoint. and opp. L s CAB, ABC,... | |
| Royal Military College, Sandhurst - Mathematics - 1890 - 132 pages
...method of proof must be geometrical. Great importance will be attached to accuracy^ 1. If a side of a **triangle be produced, the exterior angle is equal...every triangle are together equal to two right angles.** Prove the corollary with regard to the interior angles of any rectilineal figure ; and show from it... | |
| John Fry Heather - Geometry, Plane - 1890 - 172 pages
...Hence every equilateral triangle is also equiangular, and vice versa. 62. THEOE. 5. If oue side of a **triangle be produced, the exterior angle is equal...the two interior and opposite angles ; and the three** angles of every triangle are together equal to two right angles (Euc. I. 32). Hence the angles of an... | |
| Queensland. Department of Public Instruction - Education - 1890
...and of what proposition may it be regarded as the corollary '! 3. In Prop. 32, Book I., prove that **the three interior angles of every triangle are together equal to two right angles,** without producing a side of the triangle. 4. If a straight line falling on two other straight lines... | |
| Rupert Deakin - Euclid's Elements - 1891 - 79 pages
...one another. 31. To draw a straight line through a given point parallel to a given straight line. 32. **If a side of any triangle be produced, the exterior...every triangle are together equal to two right angles.** 33. The straight lines which join the extremities of two equal and parallel straight lines towards... | |
| Herbert Spencer - Psychology - 1892
...therefore also the angles CBA, BAC, ACB, are together equal to two right angles. "Therefore if aside **of any triangle be produced, the exterior angle is...and the three interior angles of every triangle are** equal to two right angles. QED" Thus in each step by which the special conclusion IB reached, as well... | |
| Euclid - Geometry - 1892 - 518 pages
...three interior angles of' a triangle are together equal to two right angles. Let ABC he a triangle, **and let one of its sides BC be produced to D : then** (i) the exterior angle ACD shall be equal to the sum of the two interior opposite angles CAB, ABC;... | |
| Yale University - 1898
...DEPARTMENT (YALE COLLEGE) GEOMETRY JUNE 1886. (Four out of five questions are required.) 1. If a side oí **any triangle be produced, the exterior angle is equal...every triangle are together equal to two right angles.** 2. (Problem) To describe a square on a given straight line. (Show clearly in the figure the methods... | |
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