 In any triangle, the product of two sides is equal to the square of the bisector of the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab = t  Exercise Manuals - Page 60by George Albert Wentworth - 1889Full view - About this book
 | George Albert Wentworth - 1884 - 264 pages
...opposite sides. Let ABCD be the quadrilateral. In AC take a point E such that Z EDC= /. ADB. A ADB and CDE are similar; also, the A BCD and ADE. From these triangles...and join BE. A ACD and ECB are similar ; also- see No. 1G4. 19. In every triangle the sum of the squares of two sides is equal to twice the square of... | |
 | George Albert Wentworth - 1886 - 264 pages
...quadrilateral. In AC take a point E such that Z EDC=* Z ADB. A ADB and CDE are similar; also, the & BCD and ADE. From these triangles obtain equations...and join BE. A ACD and ECB are similar; also, see No. 164. 19. In every triangle the sum of the squares of two sides is equal to twice the square of... | |
 | George Albert Wentworth - 1889 - 264 pages
...in A, B, C, the other in D, E, F, respectively. Prove that the triangles ABC, DJSFaxe similar. 16. In every triangle the product of two sides is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side. If AC, BCare... | |
 | George Albert Wentworth - 1898 - 264 pages
...quadrilateral. In AC take a point E such that /. EDC= /. ADB. A ADB and CDEare similar; also, the &BCD , and ADE. From these triangles obtain equations involving...and join BE. A ACD and ECB are similar ; also, see No. 164. 19. In every triangle the sum of the squares of two sides is equal to twice the square of... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...20, and 18, respectively. Find the length of the median to 18. PROPOSITION XL. THEOREM 328. In any triangle, the product of two sides is equal to the...the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab... | |
 | Arthur Schultze - 1901 - 260 pages
...20, and 18, respectively. Find the length of the median to 18. PROPOSITION XL. THEOREM 328. In any triangle, the product of two sides is equal to the...the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...20, and 18, respectively. Find the length of the median to 18. or PROPOSITION XL. THEOREM 328. In any triangle, the product of two sides is equal to the...the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...parallelogram is equal to the sum of the squares of the diagonals. PROPOSITION XL. THEOREM 328. In any triangle, the product of two sides is equal to the...the included angle plus the product of the segments of the third side. Hyp. In A abc, the bisector t divides c into the segments, p and q. To prove ab... | |
 | George Albert Wentworth - 1904 - 264 pages
...opposite sides. Let ABCD be the quadrilateral. In AC take a point .Esuch that Z EDC= /. ADB. A ADB and CDE are similar; also, the A BCD and ADE. From these triangles...to meet the circumscribed circle in E, and join BE. A A CD and ECB are similar; also, see No. 164. 19. In every triangle the sum of the squares of two... | |
 | Levi Leonard Conant - Geometry - 1905 - 140 pages
...joining their homologous vertices are concurrent. What happens when the triangles are equal ? 510. In any triangle the product of two sides is equal to the...the segments into which it divides the third side. HINT. Produce the bisector to meet the circumscribed circle, and join the point where it meets the... | |
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