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 Plane Geometry: For the Use of Schools - Page 71by Nicholas Tillinghast - 1844 - 96 pagesFull view - About this book
| George Albert Wentworth - 1881 - 266 pages
...squares on the diagonals. GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 3-41. Two triangles having **an angle of the one equal to an angle of the other** are to each other an the products of the sides including the equal angles. Let the triangles ABC and... | |
| Great Britain. Education Department. Department of Science and Art - 1882 - 512 pages
...the 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... | |
| Isaac Sharpless - Geometry - 1882 - 292 pages
...(V. 4) similar. Proposition 6. Theorem. — 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 will be similar. Let the triangles ABC, DEF have the angle A equal to the angle D, and... | |
| Mathematical association - 1883 - 86 pages
...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... | |
| Edward Olney - Geometry - 1883 - 354 pages
...Fig. 183. PROPOSITION V. 373. Theorem.— Two triangles having an angle in one equal to an' angle in **the other, and the sides about the equal angles proportional, are similar.** •' ' > AC DF CB FE' DEMONSTRATION. Let ABC and DEF have the angle* C and F equal, and We are to prove... | |
| University of Glasgow - 1883 - 438 pages
...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 - 242 pages
...NAM equal to SB. Draw AO parallel to BC. 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- _ eluding the equal angles. See Theo. VII. BAC :... | |
| Mathematical association - 1884 - 146 pages
...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... | |
| Henry Martyn Taylor - 1893 - 486 pages
...is to CD as EF to GH. (V. Prop. 16.) Wherefore, if the ratio ,fec. PROPOSITION 23. If two triangles **have an angle of the one equal to an angle of the other,** tlte ratio of the areas of the triangles is equal to the ratio compounded of the ratios of the sides... | |
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