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If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Plane and Solid Geometry - Page 45
by Arthur Schultze, Frank Louis Sevenoak - 1902 - 370 pages

Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...distant from its sides. THEOREM XXVII. 92. If two triangles have two sides of one equal rospectively to two sides of the other, but the included angle...first greater than the included angle of the second, the third side of the first is greater than the third side of the second. In the triangles ABC and...

Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...perimeter of the star is greater than that of the polygon ABCDEF. PROPOSITION XXVIII. THEOREM 181. If two triangles have two sides of the one equal respectively to two sides of the other, and the included angles unequal; the third sides are unequal, and the greater third side belongs to...

Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 392 pages
...process can be repeated until a triangle is reached. 571. EXERCISE. Two triangles are equivalent if they have two sides of the one equal respectively to two sides of the other, and the included angles supplementary. [Place the A so that the two supplementary A are adjacent and...

Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - Geometry - 1904 - 324 pages
...the angle between equal sides bisects at right angles the third side. 511. Theorem. If two spherical triangles have two sides of the one equal respectively to two sides of the other, and the angles opposite one pair of equal sides equal, then the angles opposite the other pair are...

Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - Geometry - 1904 - 313 pages
...the angle between equal sides bisects at right angles the third side. 511. Theorem. If two spherical triangles have two sides of the one equal respectively to two sides of the other, and the angles opposite one pair of equal sides equal, then the angles opposite the other pair are...

Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...greater angle at the center) . .-. chord AB > chord DF, Art. 107. (if two A have two sides of one equal to two sides of the other, but the included angle of the first greater, etc.). CONVERSELY. Given the equal circles 0 and O', and chord AB > chord DF. To prove arc AB > arc...

Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...greater angle at the center) . /. chord AB > chord DF, Art. 107. (if two A have two sides of one equal to two sides of the other, but the included angle of the first greater, etc.). CONVERSELY. Given the equal circles 0 and Of, and chord AB > chord DF. To prove arc AB > arc...

Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
....-. AACD is equilateral (why ?), and AD, half of AB = AC. .:AB=2AC. Ex. 23. 7/' two triangles hace two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal...