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" If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. "
An Easy Introduction to the Mathematics: In which the Theory and Practice ... - Page 281
by Charles Butler - 1814
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...subtracted from two right angles, the remainder is equal to the third angle. 140. COR. 2. If two triangles have two angles of the one equal to two angles of the other, the third angles are equal. 142. COR. 4. In a triangle there can be but one rigid angle, or one obtuse...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 356 pages
...produced, pass through the centre. 2. Prove one case of the following proposition : — If two triangles have two angles of the one equal to two angles of the other, each to each; and one side equal to one side, viz., either the sides adjacent to the equal angles in each, or sides...
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Treatise on Trigonometry ...

William Ernest Johnson - Plane trigonometry - 1889 - 574 pages
...draw IX, IT, IZ perpendiculars on the sides. Then, the triangles BXI, BZ1 having a common side BI and two angles of the one equal to two angles of the other, are equal in all respects, so that IX=IZ. Similarly IX=IY, :.IY=IZ. Therefore, the triangles AZI, A...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Prop. 8. From what Proposition is it an immediate inference ? PROPOSITION 26. THEOREM. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely, either the sides adjacent to the equal angles or sides which...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...that BC < EF. AA It remains .'. that A > D. Proposition 26. (First Part.) THEOREM — If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the two sides adjacent to these angles equal ; then the triangles are identically...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...third angle can be found by subtracting this sum from two right angles, 100. COR. 3. If two triangles have two angles of the one equal to two angles of the other, the third angles are equal. 101. COR. 4. A triangle can have but one right angle, or but one obtuse...
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Rider Papers on Euclid (books I. and II.)

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...to P, the angle ACB equal to Q, and AX the perpendicular from A to the base BC. 6. If two triangles have two angles of the one equal to two angles of the other, each to each, then the third angle of the one is equal to the third angle of the other. XVI. 1. In the figure of...
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 188 pages
...Proposition 25, deduce the truth of Proposition 24. *-• Proposition 26. Part II. 104. If two triangles have two angles of the one equal to two angles of the other each to each, and the side opposite to an equal angle of the one equal to the corresponding angle of the other, then...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...acute, according as AB is greater or less than AC. PROPOSITION 26. THEOREM. If two triangles have trto angles of the one equal to two angles of the other, each to each, and a side of one equal to a side of the other, these sides being either adjacent to the equal angles,...
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Elementary Synthetic Geometry

George Bruce Halsted - Geometry - 1896 - 208 pages
...opposite angles are supplemental. 403. Theorem. Two spherical triangles, of the same sense, having two angles of the one equal to two angles of the other, the sides opposite one pair of equal angles equal, and those opposite the other pair not supplemental,...
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