 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 be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'.  Elements of Plane and Solid Geometry - Page 44by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
 | Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...CF. Hence, in the triangles ACE and ACF, AE equals AF. Hence, finally, in the triangles ABE and ABF, the three sides of the one are equal respectively to the three sides of the other, and therefore the angles ABE and ABF are equal. QED 45 66. COROLLARY 2. An oblique line makes with... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...equal respectively to a side and homologous acute angle of the other. • PROPOSITION XV. THEOREM. 91. Two triangles are equal when the three sides of the...equal respectively to the 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... | |
 | George Albert Wentworth - Geometry - 1898 - 266 pages
...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 sidles of the other. In the triangles ABC and A'B'C', let AB = A'B', AC = A'C', £C=B'C'. Proof. Place... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...bisects the vertical angle of the triangle. PROPOSITION XXIV. THEOREM. 150. 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 be equal to A'B', AC tc A'C', BC to B'C'. To prove that A ABC... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...triangle bisects the base, and bisects the vertical angle of the triangle. 150. Two triangles are equal if the three sides of the one are 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,... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...of the triangle. BOOK I. PLANE GEOMETRY. PROPOSITION XXIV. THEOREM. 150. 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 be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...contrary to the hypothesis. Therefore, ZC must be greater than Z F. PROPOSITION XXVI. — THEOREM. Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. Given. — Let ABC and DEF be two triangles, having... | |
 | Education - 1902 - 780 pages
...the line that cuts off the greater distance is the longer. 2 Prove that two triangles are equal if the three sides of the one are 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... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...opposite the equal angles are equal, and the triangle is isosceles. 150. Two triangles are equal if the three sides of the one are 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,... | |
 | James Howard Gore - Geometry - 1902 - 266 pages
...and homologous acute angle of the other. PROPOSITION XV. THEOREM. 91. Two triangles are equal ivhen the three sides of the one are equal respectively to the 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... | |
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