Books Books
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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw...
Elements of Plane Geometry: For the Use of Schools - Page 71
by Nicholas Tillinghast - 1844 - 96 pages

## Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...triangle AGH is similar to ABC ; therefore DEF is also similar to ABC. Hence, If any two triangles have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, those two triangles are similar. PROPOSITION XXI. THEOREM. Two...

## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. — Equal triangles which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2) triangles which have an angle...

## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...properties of triangles include, by implication, those of all figures. FROPOSITION XIX. THEOREM.Two triangles, which have an angle of the one equal to an angle of tlie other, and the sides containing those angles proportional, are similar, In the two triangles ABC,...

## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional. Given two equal triangles ABC, ADE, having equal angles at A. Place the...

## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...right, since they are equal to these right angles (by Prop. 34.) CoR. 2. — If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles will be also equal ; for the angles which are opposite to these equal angles are...

## Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...must also be proportional to the sides GH, HK ,( B. IV, Def. 3). Therefore the two triangles ABC, GHK have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently these triangles are similar ; and being similar, we have...

## Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 324 pages
...Trapezoid— -consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having an angle of the one equal to an angle of the other — consequence • 93 4. Exercises.... 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE,...

## Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...the general properties of triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. 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. In the two triangles ABC, DEF, let the angles A...