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 - Page 65by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| Mathematical association - 1883
...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... | |
| University of Glasgow - 1883
...side of the second square ? 12. Prove that if two triangles have one angle of the one equal to one **angle of the other, and the sides about the equal angles proportional,** the triangles are similar. 14. One of the parallel sides of a trapezoid is double the other. Prove... | |
| Evan Wilhelm Evans - Geometry - 1884 - 149 pages
...to DGE ; hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM XI. Two triangles **having an angle of the one equal to an angle of the other, and the sides about** those angles proportional, are similar. Let the two triangles ABC, DEF, have the angle A equal to the... | |
| Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...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
...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... | |
| William Kingdon Clifford - Mathematics - 1885 - 271 pages
...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 take up... | |
| Lewis Carroll - Geometry - 1885 - 318 pages
...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 - Geometry - 1887 - 322 pages
...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... | |
| Dalhousie University - 1888
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles have **an angle of the one equal to an angle of the other, and** have their areas proportional to the squares of the side* opposite these equal angles, they must be... | |
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