 | John Carroll (art master.) - Geometry - 1881 - 100 pages
...&c. :; HO LESSON XIX.— RECTILINEAL FIGURES INSCRIBED IN AND DESCRIBED ABOUT OTHERS— Continued. " The opposite sides (and angles) of a parallelogram are equal to one another." — Euclid i. 34. Problem 118. — Within any quadrilateral figure V WX Y to inscribe a parallelogram,... | |
 | John Gibson - 1881 - 64 pages
...be parallel to the base, prove that the triangle is isosceles. TEST PAPER E. Propositions 33-40. 1. The opposite sides and angles of a parallelogram are equal to one another. 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. Triangles... | |
 | John Carroll (art master.) - Geometry - 1881 - 100 pages
...Fig.lU. wzv LESSON XIX.— RECTILINEAL FIGURES INSCRIBED IN AND DESCRIBED ABOUT OTHERS— Continued. " The opposite sides (and angles) of a parallelogram are equal to one ,_ another." — Euclid i. 34. Problem 118. — Within any quadii'lateral figure VWXY to inscribe a... | |
 | Marianne Nops - 1882 - 278 pages
...shown 'to be equal to it. Wherefore the straight lines, &c. — QED PROPOSITION XXXIV., THEOREM 24. The opposite sides and angles of a parallelogram are...equal to one another, and the diameter bisects it. Let ACDB be a Ig*m. of which BC is a diameter. Then shall AB = DC, and AC = DB. And L BAG = L CDB,... | |
 | Mary W I. Shilleto - 1882 - 418 pages
...two given points draw two lines, forming with a line given in position, an equilateral triangle. 3. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects the parallelogram, that is, divides it into two equal parts. If from the base to the... | |
 | 1882 - 486 pages
...of that which has the greater contained angle is greater than the base of the other. 8. Prove that the opposite sides and angles of a parallelogram are equal to one another ; and that the diagonal of a parallelogram bisects it. 4. On a given straight line construct a parallelogram... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...angles ; therefore AC is parallel (I. 25) to BD, and ABDC is a parallelogram (Def. 22). Proposition 32. Theorem. — The opposite sides and angles of a parallelogram are equal to each other, and the diagonal bisects it. Let ABD C be a parallelogram ; then will its opposite sides... | |
 | Euclides - 1883 - 176 pages
...sides of a triangle, they shall form a triangle equiangular to the given triangle. PROP. 34. THEOR. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it. Given ABCD, a parallelogram, AB ie, given AB || DC, and AD || BC; let AC be joined.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...whole angle A CD. [A x. 2. And the angle BAG has been shewn to be equal to the angle CDB. Therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter bisects the parallelogram. For AB being equal to CD, and BG common, the two sides... | |
 | Moffatt and Paige - 1883 - 516 pages
...is equal to the whole angle ACD (Ax. 2). And the angle BAG has been proved equal to BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter BC bisects it. For since, in the triangles ABC, BCD, AB is equal to CD, and BC is... | |
| |
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. 
