 | Euclides - 1883 - 176 pages
...AB at E. Prove that EDB is an isosceles triangle. For Euclid I. 30, see Appendix. PROP. 30. THEOR. Straight lines which are parallel to the same straight line are parallel to one another. Given AB || CD, and EF || AB CD. To prove AB || EF. s If AB is not || EF, they will EF... | |
 | Euclides - 1884 - 214 pages
...equal to two right angles. Axiom 1. Therefore, if a straight line &o. QED PROPOSITION XXX. THEOREM. Straight lines which are parallel to the same straight line are parallel to each other. GIVEN that AB ami CD are each parallel to EF; 11 IS REQUIRED TO PROVE that AB is parallel to CD. Draw... | |
 | Henry Elmer Moseley - Universities and colleges - 1884 - 214 pages
...2. Prove that the angles at the base of an isosceles triangle are equal to each other. 3. Prove that straight lines which are parallel to the same straight line are parallel to each other. 4. Prove that the diagonals of a parallelogram bisect each other. 5. Inseribe a trapezium ABCD in a... | |
 | Euclides - 1884 - 434 pages
...draw DE _L AC, and meeting CB at E. From E draw EF _L DE and = EC; join CF. PROPOSITION 30. THEOREM. Straight lines which are parallel to the same straight line are parallel to one another. AB CD Let AB and CD be each of them || EF: it is required to prove AB \\ CD. If AB and... | |
 | Euclides - 1884 - 182 pages
...on opposite aides of HC ; then show that AB and CD are parallel. 72. PROPOSITION XXX. — THEOREM. Straight lines which are parallel to the same straight line are parallel to one another. Let the straight lines AB, CD be each of them parallel ioEF. Then shall AB be also parallel... | |
 | Stewart W. and co - 1884 - 272 pages
...right angles; therefore also BGH, GHD, are equal to two right angles. XXX. — Straight lines wJnch are parallel to the same straight line are parallel to each other. Let AB, CD, be each of them parallel to EF; AB is also parallel to CD, Let the straight line GHK cut... | |
 | James Maurice Wilson - Conic sections - 1885 - 180 pages
...perpendicular by the first part of theTheorem : therefore the perpendicular is the parallel. THEOREM 8. Straight lines which are parallel to the same straight line are parallel to one another '. Let A and B be each of them parallel to C; then shall A be parallel to B. Proof. Take... | |
 | Canada. Department of the Interior - 1888 - 756 pages
...every triangle is subtended by the greater side, or, has the greater side oppdsite to it. 2. Show that straight lines which are parallel to the same straight line are parallel to each other. 3. Show that if a straight line be divided into two equal parts, and also into two unequal parts, the... | |
 | George William Usill - Surveying - 1889 - 306 pages
...one another, and also the exterior angle equal to the interior and opposite upon the same side. 17. Straight lines which are parallel to the 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... | |
 | Euclid - Geometry - 1890 - 442 pages
...+ BSR = ASR + BSR, = two rt. A 8. AA Similarly SRC + ASR = two rt. A". Proposition 30. THEOREM — Straight lines which are parallel to the same straight line are parallel to each otfier. Let st. lines AB, CD be each || to PQ. Draw XY across them, meeting AB, PQ, CD in _ f D~ R»... | |
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Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles. 
