 If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.  Pure mathematics - Page 119by Edward Atkins - 1874Full view - About this book
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...equal to it. In that case, CAI and EDF would be together equal to two right angles. PROP. XXV. THEOR. If a side of any triangle be produced, the exterior...equal to the two interior and opposite angles ; and (he three interior angles of every triangle are equal to two right angles. Let ABC be a triangle, and... | |
 | Mathematics - 1835 - 684 pages
...(o) The three angles of a triaugle are together equal to two right angles; and if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles . 14 (/>) In a right angled triaugle — 1. One of the angles, viz. the right angle, is equal to the... | |
 | John Playfair - Geometry - 1836 - 148 pages
...therefore, also, the angles CBA, BAC, ACB, are equal to two right angles. Wherefore, if a side of a tqangle be produced, the exterior angle is equal to the two...angles of every triangle are equal to two right angles. Which was to be proved. COR. I. All the interior angles of any rectilineal figure, together with four... | |
 | Mathematics - 1836 - 488 pages
...XXX. Straight lines which are parallel to the same straight line are parallel to one another. XXXII. If a side of any triangle be produced, the exterior angle is equal to the two interior and op. posite angles ; and the three interior angles of every triangle are equal to two right angles.... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...straight line / through a given point parallel to a g - f, given straight line. PROPOSITION XXXII. Theorem. If a side of any triangle be produced, the...angles of every triangle are equal to two right angles. Steps of the Demonstration. 1. Prove that the altern. Z BAC = alternate Z ACE, And since AB, CD are... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...EAF is drawn through the given point A parallel to the given straight line BC. PROP. XXXII. THEOR. / If a side of any triangle be produced, the exterior...interior angles of every triangle are equal to two rightfmgles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the exteripr angle... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...line equal to that which is described by either extremity of the base.* BOOK I. PROP. XXXII. THEOR. IF a side of any triangle be produced, the exterior angle is equal to the two interior and remote angles ; and the three interior angles of every triangle are together equal to two right angles.... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...the exterior angle is greater than either of the interior and opposite angles. 7. If one side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles. 8. If each of the sides of a triangle be produced, the three exterior angles are, together, equal to... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...A parallel to the given straight line BC. PROPOSITION XXXII. THEOREM. If a side of any triangle he produced, the exterior angle is equal to the two interior and opposite angles ; and vie three interior angles of every triangle are equal to two right angles. Let ABC he a triangle, and... | |
 | Euclid - Geometry - 1838 - 470 pages
...given point A parallel to the given straight line BC. Which was to be done. PROP. XXXII. THEOR. Ir a side of any triangle be produced, the exterior angle...angles of every triangle are equal to two right angles. ROOK I. triangle, viz. ABC, BCA, CAB, are together equal to two right angles. Through the point C draw... | |
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