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
| Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...of the first. For example, the converse of Theorem 1 is as follows : If two triangles are congruent, **two sides and the included angle of one are equal respectively to two sides and the included angle** of the other. EXERCISES 18. State the hypotheses of Theorems 1 to 10 inclusive. State the conclusions.... | |
| United States. Office of Education - 1921 - 1286 pages
...entire freedom in state-, ment and sequence. A. THEO It EMS. 1. Two triangles are congruent if ' (a) **two sides and the included angle of one are equal, respectively, to two sides and the included angle** of the other; (o) two angles and a side of one are equal, respectively, to two angles and the corresponding... | |
| Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...or on equal spheres, two spherical triangles are either congruent or symmetrical and equivalent when **two sides and the included angle of one are equal respectively to two sides and the included angle** of the other. Use a method similar to that used in Prop. 332. Proposition 334 Theorem On the same sphere,... | |
| Education - 1921 - 1190 pages
...favors entire freedom in statement and sequence. A. THEOREMS. 1. Two triangles are congruent if ' (a) **two sides and the included angle of one are equal, respectively, to two sides and the included angle** of the other; (l>) two angles and a side of one are equal, respectively, to two angles and tlie corresponding... | |
| Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...the included angle equal to x. NOTE. The construction and proof are to be given by the student. 164. **Theorem. Two parallelograms are congruent if two sides...equal respectively to two sides and the included angle** of the other. FIG. 179 Given the parallelograms ABCD and A'B'C'D', with AB equal to A'B', AD equal... | |
| National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...favors entire freedom in statement and sequence. A. THEOREMS. 1. Two triangles are congruent if 1 (a) **two sides and the included angle of one are equal, respectively, to two sides and the included angle** of the other; (6) two angles and a side of one are equal, respectively, to two angles and the corresponding... | |
| Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...intersection of the diagonals of a parallelogram is the center of symmetry of the parallelogram. THEOREM 35. **Two parallelograms are congruent if two sides and the included angle of one are equal** to two sides and the included angle of the other. THEOREM 36. If a quadrilateral has one side equal... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...the sup. of Z 4, and £DE is a st. line. A ABD =s A CBD. PROPOSITION III. THEOREM 69. Two triangles **are congruent if two sides and the included angle...equal respectively to two sides and the included angle** of the other (sas = sas). Given A ABC and A'B'C' with AB = A'B', BC=B'C', and B = ZB'. To prove A ABC... | |
| Laurence Ladd Buermeyer, Laurence Buermeyer - Thought and thinking - 1923 - 372 pages
...= BD, by definition of a square. Hence triangle FBC = triangle ABD, because 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. Because the angles GAB and BAG are both right angles, GA and AC are in the same straight... | |
| Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 pages
...experiment can be stated as a theorem, and proved by actual superposition. *56. Theorem. Two triangles **are congruent if two sides and the included angle...equal respectively to two sides and the included angle** of the other. Given the &ABC and DEF with AC = DF, AB = DE, and ZA = ZD. (Use Fig. 1 and Fig. 3, §... | |
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