 P' two parallels, and T, a transversal. To prove that any Z c equals its alternate Z a'. Proof. 1. Suppose Z c > Z. a!, and that Q is drawn as in the figure, making an Z equal to Z a'.  New Plane Geometry - Page 46by Wooster Woodruff Beman, David Eugene Smith - 1899 - 252 pagesFull view - About this book
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...or fill the same space, are equal to each other. 7. Halves of the same are equal to each other. 11. Two intersecting straight lines cannot both be parallel to the same straight line, or to each other. Illustration of the Definitions. The angular point is marked by a letter, and when... | |
 | Euclid - Geometry - 1890 - 442 pages
...the third side. Many substitutes for this axiom have been suggested : the best of them is this — "Two intersecting straight lines cannot both be parallel to the same straight line." All the propositions about parallels can be deduced from this last axiom. It will be a good exercise... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...17. The student may perhaps find less difficulty in admitting as an evident truth the statement that 'Two intersecting straight lines cannot both be parallel to the same straight line,' or ' Through a given point only one parallel can be drawn to a given straight line,' from either of... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...angles ; therefore AB is parallel to CD. (Prop. 27.) Wherefore, straight lines ,fec. EXERCISES. 1. Two intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...equal to Z a'. 2. Then Q would be parallel to P'. Why ? 3. But this is impossible, '.' P II P'. Post. 5 (Two intersecting straight lines cannot both be parallel to the same straight line.) 4. Similarly it is absurd to suppose that Z a' > Z c. COROLLARIES. 1. A line perpendicular to one of... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...to /_ a'. 2. Then Q would be parallel to P'. Why ? 3. But this is-impossible, '.- P II P'. Post. 5 (Two intersecting straight lines cannot both be parallel to the same straight line.) 4. Similarly it is absurd to suppose that Z a' > Z c. .'.Zc = Za'. COROLLARIES. 1. A line perpendicular... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...alternate angles ; therefore AB is parallel to CD. (Prop. 27.) Wherefore, straight lines &c. EXERCISES. 1. Two intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
...draughtsman's square slides along a ruler, as in the annexed figure, BiCi II B2C2, and AiCi II A2C3. 85. Postulate of Parallels. It now becomes necessary...necessarily true if the postulate is.) PROPOSITION XVII. 2^~ 86. Theorem. The alternate angles formed by a transversal with two parallels are equal. Given P... | |
 | William James Milne - Geometry - 1899 - 326 pages
...KHC = 149°, and, § 69, Z Я"</Ж = Z ítfZ, = 143° ; hence, CD and £F are not parallel. Ex. 33. Two intersecting straight lines cannot both be parallel to the same straight line. Proof. If the lines could be parallel to the same straight line, § 80, they would be parallel to each... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...to Z a'. 2. Then Q would be parallel to P' . Why? 3. But this would be impossible, v P II /". § 85 (Two intersecting straight lines cannot both be parallel to the same straight line.) 4. Similarly, it is absurd to suppose that Z a' > Z c. .'.Zc=Za'. COROLLARIES. 1. A line perpendicular... | |
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