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 Boeken Boek 61 - 70 van 193 over Two triangles, which have an angle of the one equal to an angle of the other, and.... Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. The Elements of geometry; or, The first six books, with the eleventh and ... - Pagina 143
door Euclides - 1855
Volledige weergave - Over dit boek ## New Elementary Geometry with Practical Applications

Benjamin Greenleaf - 1874 - 176 pagina’s
...the triangle ABC; hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have...
Volledige weergave - Over dit boek ## The elements of geometry, in eight books; or, First step in applied logic

1874
...of homologous angles are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which have an angle of the one equal to an angle of the other, have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC...
Volledige weergave - Over dit boek ## Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

James Bryce - 1874
...sides. Cor. 2. — If the two triangles are equal, ABxAC=POxOQ, therefore ^? - 29 \)L .AO that is, equal triangles which have an angle of the one equal to an angle of the other, have the sides ahout the equal angles reciprocally proportional. Cor. 3. — Hence also equiangular...
Volledige weergave - Over dit boek ## The Elements of Euclid, containing the first six books, with a selection of ...

...of the intercepted area, according as they intersect internally or externally. 15. If two trapeziums have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining...
Volledige weergave - Over dit boek ## Report, Volumes 11-20

1876
...polygons. Prove that two triangles are similar when they are mutually equiangular. 2. Two triangles having 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. 3. To inscribe A circle in a given...
Volledige weergave - Over dit boek ## Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...same demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then the sides which contain the angle of the first are the extremes of a proportion of which the sides...
Volledige weergave - Over dit boek ## Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - 1876 - 372 pagina’s
...proportionality of sides involve equality of angles. 230. Proposition XXI.— Theorem. Two triangles having an angle of the one equal to an angle of the other, and tlie including sides proportional, are similar. In the triangles, ABC, DEF, let A = D, and AB :...
Volledige weergave - Over dit boek ## SYLLABUS OF PLANE GEOMETRY

1876
...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...
Volledige weergave - Over dit boek ## Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 398 pagina’s
...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...
Volledige weergave - Over dit boek ## Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 443 pagina’s
...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...
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