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" There are three important theorems in geometry stating the conditions under which two triangles are congruent: 1. Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the... "
Plane Geometry - Page 72
by John Charles Stone, James Franklin Millis - 1916 - 278 pages
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California Education, Volume 2

Education - 1914 - 220 pages
...long AB and AC are drawn, or what size angle A has? This proves Theorem II. Two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. Problem V. To construct a triangle when two sides and their included angle are given....
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...manner. If ZA OL = 80, how many degrees are there in the other A'! 52. THEOREM. Two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. c BR Given : A ABCnm\RST; AB = ES; AC = RT; ZA = Z R. To Prove : A ABC = A RST. Proof...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...manner. If ZA OL = 80, how many degrees are there in the other Al 52. THEOREM. Two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. c T BR Given: A ABC&ndRST; AB = RS; AC = RT; ZA = Z R. To Prove : A ABC = A RST. Proof...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...other. 683. Two triangles on the same sphere, or on equal spheres, are either congruent or symmetrical, if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. 684. Corollary. Two symmetrical isosceles spherical triangles are congruent. 686. The...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 336 pages
...intersect, Conclusion. The vertical angles are equal. PROP. II. THEOREM 46. Two triangles are equal when two sides and the included angle of one are equal respectively to two sides and the included angle of (he other. a Draw any A ABC : draw line DE equal to AB: construct Z EDGf equal to ZA, the constructed...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 208 pages
...tlieu use 106.) PROP. XXXVI. THEOREM • ~j 110. Two parallelograms are equal when two adjacent sides and the included angle of one are equal respectively to two adjacent sidv and the included angle of the other. f E* Draw [U ABCD and EFGH in accordance with the...
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First-year Mathematics for Secondary Schools

Ernst Rudolph Breslich - Mathematics - 1909 - 402 pages
...made to coincide. Exercises 1, 2, and 3 illustrate the following theorem: 274. Theorem: Two triangles are congruent if two sides and the included angle...equal respectively to two sides and the included angle of the other. The truth of this statement may be established by reasoning as follows: Let ABC and C...
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Key to the Exercises in Wells's New Geometry

Webster Wells - 1909 - 154 pages
...intersection is perpendicular to the other.) 387. 3. Hence, AKTJ=AKTL. (Two triangles are equal when two sides and the included angle of one are equal respectively to two sides and the included angle of the other.) 46. 4. Hence, KJ = KL. (In equal figures the homologous parts are equal.) 48....
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...a parallelogram. Ex. 33. The diagonals of a rectangle are equal. PROPOSITION XLIII. _ THEOREM. 176. Two parallelograms are congruent if two sides and...respectively, to two sides and the included angle of the other. Given the Os ABCD and EFGH, with sides AB = EF, AD = EH, and the A = E. To prove...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...is a parallelogram. Ex. 33. The diagonals of a rectangle are equal. PROPOSITION XLIII. THEOREM. 176. Two parallelograms are congruent if two sides and...included angle of one are equal, respectively, to t,vo sides and the included angle of the other. Given the Os ABCD and EFGH, with sides AB = EF, AD...
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