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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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'.
Plane Geometry - Page 180
by Arthur Schultze - 1901

## Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

...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...

## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...4 ÊF* = AC1 + SD* + 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the other are to each other as the products cf t he sides including the equal angles. Let the triangles ABC and ADE have the common angle A. We...

## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...4 = AC? + BI? + 4 ^ QED GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the other are to each other as tAe products of the sides including the equal angles. D. Let the triangles ABC and ADE have the common...

## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...value. Ex. 1. Show that two triangles which have an angle of the one equal to the supplement of the angle of the other are to each other as the products of the sides including the supplementary angles. С \j 2. Show, geometrically, that the square described upon the sum of two straight...

## An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...are respectively similar. 112. Two tetraedrons having a triedral angle of the one equal to a triedral angle of the other are to each other as the products of the edges of the equal triedral angles. (70 ; II. 116, 55.) 113. State and prove the converse of Theorem...

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

Elias Loomis - Conic sections - 1877 - 458 pages
...the point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they have an angle of the one equal to an angle of the other, and the sides including those angles proportional. Let the triangles ABC, DEF have the angle A of the...

## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the oiher are to each other as the products of the sides including the equal angles. Д Let the triangles ABС and ADE have the common angle A. Tjr , АABС ABX AС \\ e are to prove =...

## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 436 pages
...EH AE = B'C'' A'B' B'C' =A'B', Hyp. Ax. 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles having an angle of the one equal to an angle of the other, and the including sides proportional, are similar. A A' In. the triangles ABC and A' B' С' let /А...