 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...two equal and parallel straight lines towards the same parts are themselves equal and parallel. 34. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects the parallelogram, ie divides it into two equal parts. 35. Parallelograms on the same base and between... | |
 | Edward Travers Dixon - Geometry - 1891 - 180 pages
...the perpendicular to CD, and is equal to AB. Therefore The perpendicular &c. QED PROPOSITION XXIII. The opposite sides and angles of a parallelogram are equal to one another. For if ABDC be a parallelogram, AB is parallel to CD. [D 13. Let X in CD be the point in the same direction... | |
 | Queensland. Department of Public Instruction - Education - 1892 - 508 pages
...sides equal to three given straight lines, any two of which aro together greater than the third. 18 4. The opposite sides and angles of a parallelogram are equal to one another, and each diagonal bisects the parallelogram. 15 5. To describe a parallelogram that shall he equal to a... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...are equal respectively to the three sides of the other. For those offering two books of Euclid. 3. The opposite sides and angles of a parallelogram are equal to one another and the diagonal bisects the parallelogram. 4. If a straight line be divided into two equal parts and also... | |
 | Frederick Coate Wade - Catholic Church Education Manitoba - 1895 - 168 pages
...the third side. The difference between any two sides of a triangle is less than the third side. 2. The opposite sides and angles of a parallelogram are equal to one another and the diagonal bisects it ; that is^divides it into two equal parts. Define a rhombus, an oblong, a scalene... | |
 | Seymour Eaton - 1899 - 362 pages
...it ? 8. Divide a right-angled triangle into two isosceles triangles. Lesson No. 16 PROPOSITION 34. THEOREM The opposite sides and angles of a parallelogram are equal to one another and the diagonal bisects it — that is, divides it into two equal parts. Proof . Because AB is parallel to... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...DEFINITION. A Parallelogram is a four.sided figure whose opposite sides are parallel. PROPOSITION 34. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and each diagonal bisects the parallelogram. AB CD Let ACDB be a parallelogram, of which BC is a diagonal.... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...not violate Euclid's sequence of propositions. Great importance will be attached to accuracy, .] 1. The opposite sides and angles of a parallelogram are equal to one another. 2. The complements of the parallelograms which are about the diameter of any parallelogram, are equal... | |
 | 1903 - 898 pages
...+ c. (ii) the equation whose roots are h + c, k — c. GEOMETRY. Time : three hours. 1. Prove that the opposite sides and angles of a parallelogram are equal to one another, and that a diagonal divides the parallel* gram into two equal triangles. Prove that two straight lines... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...parallel : I. 27. and it has been shewn that they are also equal. PROPOSITION 34. THEOREM. The apposite sides and angles of a parallelogram are equal to one another, and each diagonal bisects the parallelogram. AB Let ACDB be a parallelogram, of which BC is a diagonal.... | |
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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax. 
