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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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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...conversely. 25. A scalene triangle cannot have two equal angles. Geom. — 3 34 PROPOSITION X. THEOREM. 69. Two triangles are equal if the three sides of the one are respectively equal to the three sides of the other. Given: In triangles ABC, A'B'C', AB equal to A'B',...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle. 160. Two triangles are equal if the three sides of the...equal respectively to the three sides of the other. 161. Two right triangles are equal if a side and the hypotenuse of the one are equal respectively to...
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Elementary Solid Geometry and Mensuration

Henry Dallas Thompson - Geometry, Solid - 1896 - 224 pages
...equal to Z>.£, and the side AB to DF, and the side (75 to EF, wherefore, in the triangles ABC and DFE, the three sides of the one are equal respectively to the three sides of the other triangle, and thus the triangles are equal, and the angles of one triangle are equal respectively to...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...homologous acute angle of the other. • PROPOSITION XV. THEOREM. 91. Two triangles are equal when the three sides of the one are equal respectively...three sides of the other. In the triangles ABC and DEF, AB = DE, AC = DF, and To prove that the two triangles are equal. Apply the triangle ABC to DEF...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1898 - 462 pages
...is less than the perimeter, but greater than half the perimeter. PROPOSITION XXXIII. THEOREM. 160. Two triangles are equal if the three sides of the one are equal respectively to the three aides of the other. B In the triangles ABC and A'BTC', let AB = A'B', AC=A'C', To prove t Proof. Place...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...isosceles triangle bisects the base, and bisects the vertical angle of the triangle. BOOK I. TLANE GEOMETRY. PROPOSITION XXIV. THEOREM. 150. Two triangles...= A A'B'C'. Proof. Place A A'B'C' in the position AB' C, having its greatest side A'C' in coincidence with its equal AC, and its vertex at B', opposite...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...a triangle are equal, the sides opposite the equal angles are equal, and the triangle is isosceles. 150. Two triangles are equal if the three sides of...equal, respectively, to the three sides of the other. 151. Two right triangles are equal if a leg and the hypotenuse of the one are equal, respectively,...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...a triangle are equal, the sides opposite the equal angles are equal, and the triangle is isosceles. 150. Two triangles are equal if the three sides of...equal, respectively, to the three sides of the other. 151. Two right triangles are equal if a leg and the hypotenuse of the one are equal, respectively,...
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Bulletin

Education - 1902 - 788 pages
...foot of the perpendicular, the line that cuts off the greater distance is the longer. 2 Prove that two triangles are equal if the three sides of the...equal respectively to the three sides of the other. 3 Prove that lines which meet in a point intercept proportional segments on two parallel lines. 4 Complete...
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University of the State of New York Bulletin

Education - 1902 - 880 pages
...foot of the perpendicular, the line that cuts off the greater distance is the longer. 2 Prove that two triangles are equal if the three sides of the...equal respectively to the three sides of the other. 3 Prove that lines which meet in a point intercept proportional segments on two parallel lines. 4 Complete...
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