 If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.  Mathematics, mechanics, heat - Page 21by American School (Chicago, Ill.) - 1903Full view - About this book
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...greater side.] PROPOSITION XXII. THEOREM 70. If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. GIVEN—AB, AC, and a, of the triangle ABC respectively equal to A'B', A'C, and... | |
 | Ephraim Hunt - Geometry - 1896 - 120 pages
...be drawn between two points. The angles opposite the equal sides are equal. Therefore, CASE I. When two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, the remaining parts are equal, each... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...AC=AC, Hyp. ^4^f=^4^r, Iden. angle CAX= angle C'^4^T. Cons. Hence triangle ACX= triangle ACX. §78 [If two triangles have two sides, and the included...two sides and the included angle of the other, the triangles are equal.] Hence XC=XC. Now BC<BX+XC. §7 [A straight line is the shortest path between... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...AC=AC, . Hyp. AX=AX, Iden. angle C4^T= angle C'AX. Cons. Hence triangle /4 CX— triangle A C'X. §78 [If two triangles have two sides, and the included...two sides and the included angle of the other, the triangles are equal.] Hence XC=XC. Now BC'<BX+XC. §7 [A straight line is the shortest path between... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...HAD + angle FAD. \? That is, angle EDF = angle EAF, or — angle BAC. That is, the triangles ABC, DEF have two sides and the included angle of the one equal respectively to two sides and the included angle of the other. Therefore they are equal; because if two triangles have two sides and the included, etc.... | |
 | Henry W. Keigwin - Geometry - 1898 - 250 pages
...) a > b) j-Same sense. > Opposite sense. TRIANGLES. INTERSECTING LINES. PROPOSITION I. THEOKEM. 44. If two triangles have two sides and the included angle...the included angle of the other, the two triangles arc equal. DX G FIG. 21. FIG. 22. Let the two triangles ABC and DEF have the sides AB, AC oi the one... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...conclusion, or that which we wish to prove must follow from the facts admitted by the hypothesis; eg: If two triangles have two sides and the included angle...two sides and the included angle of the other, the triangles are equal. What is known, or admitted to be true, about the two triangles above mentioned?... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 490 pages
...steps in the following demonstration: DEMONSTRATION OF PROP. I. (MODEL FOR PUPILS.) /. Theorem. If any two triangles have two sides and the included angle...two sides and the included angle of the other, the triangles are equal. //. Given: Д ABC and Л DEF, in which (1) AB = DE, (2) A С = D К, and (3) z... | |
 | International Correspondence Schools - Surveying - 1898 - 518 pages
...large, may be readily found by multiplying the known volume by (£) ' = j^. SURVEYING. GEOMETRY. 118O. If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, the triangles are ( equal in all their parts. Thus,... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...steps in the following demonstration: DEMONSTRATION OF PROP. I. (MODEL FOR PUPILS.) /. Theorem. If any two triangles have two sides and the included angle of the one equal respective!}' to two sides and the included angle of the other, the triangles are equal. //. Given;... | |
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