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If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Primary Elements of Plane and Solid Geometry: For Schools and Academies - Page 21
by Evan Wilhelm Evans - 1862 - 98 pages

## First Lessons in Geometry: In Two Parts

B. Marks - 1875 - 176 pages
...What do you think of the areas of the triangles ? a d I cef DEMONSTRATION. We wish to prove, that, // two triangles have two sides, and the included angle...and the included angle of the other, each to each, the two triangles are equal in all respects. Let the triangles abc and d ef have the side ab of the...

## Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...meet at C'. Lay off EA' equal to EA, and draw the arc DA'. The rightangled triangles AED and A'ED, have two sides and the included angle of the one,...and the included angle of the other, each to each; hence, they are equal in all their parts; therefore, the angle EA'D is equal to EAD, and the side DA'...

## Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 pages
...draw the arc DA'. The right• angled triangles AED and A 'ED, have two sides and the included atigle of the one, equal to 'two sides and the included angle of the other, each to each ; hence, they are equal in all their parts ; therefore, the angle EA'D is equal to EAD, and the side...

## A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1877 - 272 pages
...form of quadrilateral.] PROPOSITION XV. 301, Theorem,—Two parallelograms having two sides and tin Included angle of the one equal to two sides and the included angle of the other, each to each, are equal. DEM.—Let AC and EC be two parallelograms, with AD = EH, AB = EF, and A = E; then are they...

## Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...because AB is equal to CD, and BC is common to the two triangles ABC, BCD, the two triangles ABC, BCD have two sides and the included angle of the one equal to two sides' and the included angle of the other; therefore the side AC is equal to BD (Pr. 6), and the angle ACB to the angle CBD. And,...

## Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...AF and FE are also equal (const.), and the angles AFC and EFB are equal (Prop. XVII.). Therefore the two triangles have two sides and the included angle...and the included angle of the other, each to each, and are every way equal (Prop. IV.); the angle EBF is equal to the angle FCA. But DBG is greater than...

## Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...34). xxii. If two spherical triangles on the same sphere, or equal spheres, have tivo sides and th& included angle of the one equal to two sides and- the included angle of the other, each to each, the two triangles will be congruent or symmetrical, and hence equal (15). xxui. If two spherical triangles...

## The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...required triangle. Proposition 7. Theorem.—If two triangles have two sides and the included angle of one, equal to two sides and the included angle of the other, each to each, the triangles will be equal in all their parts. Let ABC, DEF be two triangles which have BA, AC, and...