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" If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. "
Theoretical Geometry: Based on the Various Geometry Books by Godfrey and Siddons - Page 20
by Arthur Warry Siddons, Reginald Thomas Hughes - 1926 - 173 pages
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volume 10

Encyclopedias and dictionaries - 1816 - 764 pages
...oppofite angles. COR. ». Any two angles of a triangle are together lefs than two right angles. COR. 3. If two triangles have two angles of the one equal to two angles of the other, the remaining angle of the one is equal to the remaining angle of the other, COR. 4. The two acute...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...by BD, and that the right angle BED is equal to the right angle BFD, the two triangles • EBD, FED have two angles of the one equal to two angles of the other, and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...straight line drawn from the vertex to the base, bisecting the vertical angle. PROP. XXXII. . • (xxvi.) If two triangles have two angles of the one equal to two angles of the other, the third angle of the one shall also be equal to the third angle of the other. (XXVII.) The angle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...by BD ; and because the right angle BED, is equal to the right angle BFD, the two triangles EBD, FBD have two angles of the one equal to two angles of the other ; and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...contained by the equal to them of the other. 1 Prop. XXVI. Theor. If two triangles hive twn angles of one equal to two angles of the other, each to each ; and one side equal to one side. vi¿. either the sides adjacent to the equal angles, 01 the sides opposite...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...equal to the right angle FCL ; and therefore in the two triangles FKC, FLC, there are two angles of one equal to two angles of the other, each to each, and the side FC, which is adjacent to the equiil angles in each, is common to both ; therefore the other...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 210 pages
...parallel to CD, the alternate angles, GFE, FGH, are also equal; therefore the two triangles GEF, FHG, have two angles of the one equal to two angles of the other, each to each ; and the side FG, adjacent to the equal angles, common ; the triangles are therefore equal (theorem 6) ;...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...takes place when in each triangle two sides respectively equal, form an equal angle ; and also when two angles of the one, equal to two angles of the other, are formed on an equal side. It is easy to demonstrate these propositions in the same manner as in...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...angle BAG is greater than the angle EDF. Wherefore, if two triangles, &e. QED .5- PROP. XXVI. THEOR. If two triangles have two angles of the one equal to two angles of the other, eaeh to eaeh -, and one side equal to one side, viz. either the sides adjaeent to the equal angles,...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...2. If the corresponding diameters of two equiangular parallelograms be equal to one another, also a side of the one equal to the corresponding side of the other, then shall the other opposite sides of the one be equal to the other opposite sides of the other. 3....
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