 The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw...  Elements of Geometry - Σελίδα 146των George Albert Wentworth - 1881 - 250 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 σελίδες
...ratio of AN to NB is the duplicate of the ratio of AM to MB. 2. If two triangles of equal area have an angle of the one equal to an angle of the other, prove that the sides about the equal angles are reciprocally proportional. 3. Shew how to divide a... | |
 | Mathematical association - 1883 - 86 σελίδες
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two... | |
 | Association for the improvement of geometrical teaching - 1884 - 150 σελίδες
...two adjoining sides of the one respectively equal to two adjoining' sides of the other, and likewise an angle of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC... | |
 | Evan Wilhelm Evans - 1884 - 170 σελίδες
...parallel to BC. M ANC = ACN = CAO. ANC = CBA + BAN. Complete the proof. 24. Two triangles which have an angle of the one equal to an angle of the other, are to each other as the products of the sides in- B eluding the equal angles. See Theo. VII. BAC :... | |
 | Mathematical association - 1884 - 146 σελίδες
...two adjoining: sides of the one respectively equal to two adjoining sides of the other, and likewise an ang:le of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC... | |
 | George Albert Wentworth - 1885 - 424 σελίδες
...similar. SIMILAR POLYGONS. But Since AB BC . AE EH AE A'B' B'C'' A'B' B'C ' ' = A'B', 145 Hyp. Ax 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles...of the other, and the including sides proportional, ure similar. A A' In the triangles ABC and A' B' C' let "• •" -"• ^ We are to prove A ABC and... | |
 | William Kingdon Clifford - 1885 - 310 σελίδες
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respectively equal, they must be equal in all particulars. For if we... | |
 | Lewis Carroll - 1885 - 318 σελίδες
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one equal to an angle of the other ; the Parallelograms are identically equal.' This might be a useful exercise to set ; but really it... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 σελίδες
...A' B'C', BC = AB . B'C' A'B" hence AD BC A'D' X B'C' and we have ABC A' B' C' EXERCISE. Theorem. — Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Suggestion. Let ADE and... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 336 σελίδες
...similarity of ABC and A'B'C', BC AB hence A'D and we have _. B'c' 373-- EXERCISE. ^ *• (/ Theorem.—Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. Suggestion. Let ADE and... | |
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