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 72by John Charles Stone, James Franklin Millis - 1916 - 278 pagesFull view - About this book
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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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