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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 111
by Thomas Perronet Thompson - 1833 - 150 pages
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Inventional Geometry: A Series of Problems, Intended to Familiarize the ...

William George Spencer - Geometry - 1881 - 116 pages
...make two triangles that shall be equal to each other, and yet not similar ? 137. Can you show that all triangles upon the same base and between the same parallels are equal to one another ? -.^1 MtVg( Ce•\•. l-~ s' 138. Can you place a circle, whose radius is 1J inch, so that its...
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The Cambridge Examiner, Volume 3

Education, Higher - 1883 - 536 pages
...and have one side equal to one side, then the triangles are equal in every respect. 6. Parallelograms upon the same base and between the same parallels are equal to one another. 7. Define : adjacent angles, opposite angles, vertical angles, and alternate angles ; and give examples...
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Guide to preliminary army examination

John Gibson - 1881 - 302 pages
...equal to one another, and that the diameter bisects the parallelogram. 4. Prove that parallelograms upon the same base and between the same parallels are equal to one another. 5. Prove that in any right-angled triangle ABC, the square which is described upon the side AB subtending...
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Moffatt's reprint of pupil teachers' questions, arranged by ed. of 'Papers ...

Moffatt and Paige - 1881 - 176 pages
...base BC of a triangle ABC, so that DE shall be equal to the difference of BD, C E. 5. Parallelograms upon the same base, and between the same parallels, are equal to one another. ALGEBRA. 1. Find the value of &(y + x)# + $x(y - z)' - (x - z), when .r = 3, y = 4, z = 7. 2. Simplify...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - Euclid's Elements - 1881 - 236 pages
...at the vertices of any two of its opposite angles. PROP. XXXV. THEOREM. Parallslogramt upon the tame base, and between the same parallels, are equal to one another. Let the parallelograms AC, BF be upon the same base BC, and and between the same parallels AF, BC. The parallelogram...
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The preliminary army examination made easy, a guide to self-preparation

John Gibson - 1881 - 64 pages
...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 on the same base and between the same parallels are equal. 4. Equal triangles on the same...
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Class lessons on Euclid

Marianne Nops - 1882 - 278 pages
...equal to fm0- EFGH. .-. ||""™ ABCD = ||*™m EFGH (ax. 1). Wherefore parallelograms, &c. — QED PROPOSITION XXXVII. THEOREM. Triangles upon the same...the same parallels are equal to one another. Let the As ABC, DBC be on the same base BC and between the same ||s AD, BC. A ABC shall be equal to A DBC....
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The Cambridge Examiner, Volume 2

Education, Higher - 1882 - 498 pages
...practical proof of this proposition. 7. Enunciate the propositions which tell when lines are parallel. 8. Triangles upon the same base and between the same parallels are equal to one another. 9. If the square described upon one of the sides of a triangle be equal to the squares described upon...
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The Competitor, Volumes 3-4

1883 - 248 pages
...circles of given unequal radii, so as to tonch each other, and a given straight line. 6. Parallelograms upon the same base, and between the same parallels are equal to one another. 7. In obtuse- angled triangles if a perpendicular be drawn from any one of the acute angles to the...
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The Practical Teacher, Volume 1, Issue 1

Education - 1882 - 676 pages
...equal to two right angles ; the two straight lines shall be parallel to one another. 3. Parallelograms upon the same base, and between the same parallels, are equal to one another. Arc the parallelograms equal in all respects ? Algebra. 1. Simplify ij — J{i — \(x— Ji}, and...
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