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" Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. In the triangles ABC and A'B'C', let AB = A'B', AC = A'C', BC=B'C'. To prove A ABC= A A'B'C'. Proof. Place A A'B'C' in the position AB'C, having... "
Plane Geometry - Page 38
by George Albert Wentworth - 1899 - 256 pages
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Annual Statement, Volumes 11-20

1876 - 646 pages
...text-book you have studied on the subject and to what extent.] 1. Prove that two triangles are equal when the three sides of the one are equal respectively to the three sides of the other. 2. A straight line cannot intersect the circumference of a circle in more than two points. 3. Upon...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 pages
...equal in all respects. GEOMETRY. BOOK I. PROPOSITION XXV. THEOREM. 108. Two triangles are equal when the three sides of the one are equal respectively to the three sides of the other. B B' О In the triangles AB С and A' B' C', let AB = A' B', AC = A'C', BC = B' C'. We are to prove...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...equal in all respects. GEOMETRY. BOOK I. PROPOSITION XXV. THEOREM. 108. Tuio triangles are equal when the three sides of the one are equal respectively to the three aides of the other. B B' In the triangles ABC and A' B' C', let AB = A' B', AC = A'C', BC = B'C'. We...
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Elementary Geometry: Congruent Figures

Olaus Henrici - Congruences (Geometry) - 1879 - 218 pages
...quadrilateral will be a kite if AC =AC and BC=BC ( 172). Hence Theorem : Two triangles are co?igruent if the three sides of the one are equal respectively to the three sides of the other. 187. A quadrilateral is also a kite if two adjacent sides are equal, and if the angle between them...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...in all respects. QED GEOMETRY. BOOK I. PROPOSITION XXV. THEOREM. 108. Two triangles are equal when the three sides of the one are equal respectively to the three sides of the other. В В' In the trtangles ABC and A' B' C', let AB = A' B', AC = A'C', BC^B' C'. Wearetoprove Д A BC...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...and are equal in all respects. QED PROPOSITION XXV. THEOREM. 108. Two triangles are equal when ihe three sides of the one are equal respectively to the three sides of the other. B B' In the triangles ABC and A' B' C', let AB = A' B', AC = A' C', 7? (7 = B' C'. We are to prwe AABC...
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Class lessons on Euclid

Marianne Nops - 1882 - 278 pages
...angles ECD and FDC on the other side of the base). Case III. is obvious. Proposition VIII. shows that two triangles are equal if the three sides of the one are equal to those of the other each to each. This is the second case of the equality of triangles demonstrated...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1885 - 424 pages
...coincide, and are equal in all respects. PROPOSITION XXV. THEOREM. 108. Two triangles are equal when the three sides of the one are equal respectively...three sides of the other. In the triangles ABC and A' B ' C', let AB = A ' B', AC = A'C', BC = B'C'. We are to prove A ABC = A A ' B' C'. Place A A' '...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...point common to the two lines. THE ELEMENTS OF GEOMETRY. THEOREM IX. 129. Two triangles are congruent if the three sides of the one are equal respectively to the three sides of the other. HYPOTHESIS. Triangles ABC and LMN, having AB = LM, BC = MN, and CA = NL. CONCLUSION. A ABC ^ A LMN....
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...point common to the two lines. THE ELEMENTS OF GEOMETRY. THEOREM IX. 129. Two triangles are congruent if the three sides of the one are equal respectively to the three sides of the other. HYPOTHESIS. Triangles ABC and LMN, having AB = LM, BC = MN, and CA = NL. CONCLUSION. A ABC ^ A LMN....
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