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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 30
by Euclid - 1835 - 513 pages

## The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...the diagonal is the straight line joining the vertices of two opposite angles. PROP. XXXIV. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it, that is, divides it into UEO equal parts. Let AD be a parallelogram, of...

## The Popular Educator, Volume 5

1856 - 428 pages
...to the whole angle А с D ; and the angle в А с has been proved to be equal to the angle в DC; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diagonal в с bisects the parallelogram A D. Because in the two triangles ABC and D с в, the...

## Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...point in a given straight line to make a given rectilineal angle equal to a given rectilineal angle. 4. The opposite sides and angles of a parallelogram are equal to one another and the diameter bisects them, that is, divides them into two equal parts. 6. In any right-angled triangle,...

## National Society's Monthly Paper

1858 - 380 pages
...side. Is the same proposition true of the angles of a triangle? 3. What is a parallelogram? Prove that the opposite sides and angles of a parallelogram are equal to one another, and that the diagonal bisects it. 4. If a straight line be divided into any two parts, the rectangles...

## Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...angle ABD is equal to the whole angle ACD. But the angle BAC has been proved equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to each other. Cor. Two parallels, AB, CD, comprehended between two other parallels, AC, BD, are equal...

## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...28); therefore the lines joining their extremities are equal and parallel. pROposmou xxxiv. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it; that is, divides it in two equal parts. Given a parallelogram ACDB, of...

## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...as well as those which bisect any two interior angles of a parallelogram, contain a right angle. 78. The opposite sides and angles of a parallelogram are equal to one another, and the diameters bisect it. State and prove the converse of this proposition. Also shew that a quadrilateral...

## The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...equal to the whole angle ACD; (ax. 2) and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter shall bisect it. For because AB is equal to CD; and BC common, the two AB, BC, are equal...