...Ax. 3 §351 § 351 Ax. 1 §357 BOOK III. PLANE GEOMETRY. PROPOSITION XXVI. THEOREM. 366. CONVERSELY : If two polygons are composed of the same number of...each, and similarly placed, the polygons are similar. 13' In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, BEC, CED be similar, respectively,...

...§ 351 § 351 § 351 Ax. 3 §351 § 351 Ax. 1 §357 QED PROPOSITION XXVI. THEOREM. 366. CONVERSELY: If two polygons are composed of the same number of...each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, BEC, CED be similar, respectively,...

...exterior point are equal, and make equal angles with the line ; the point to the center. 3 Prove that if two polygons are composed of the same number of...each, and similarly placed, the polygons are similar. 4 Complete and demonstrate the following : the area of a trapezoid is equal to ... 5 State the ratio...

...homologous base of a similar triangle is PROP. XX. THEOREM. 266. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Given, in polygons AC and A'C', A ABE similar to A A' B'E', A BCE to AB'C'E', and A CDE to A C'D'E'....

...CAB are similar. SIMILAR POLYGONS. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed, of the same number of triangles, similar each to each, and similarly placed. E BC Let the polygons ABCDE and A'B'C'D'B' be similar. From two homologous vertices, as E and E', draw...

...homologous base of a similar triangle is PROP. XX. THEOREM. 266. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. V Given, in polygons AC and A'C', A ABE similar to A A'B'E', ABCE to AB'C'E', and A CDE to A C'D'E'....

...triangles CED and CAB are similar. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. BC B' C Let the polygons ABCDE and A'B'C'D'E' be similar. From two homologous vertices, as E and E',...

...triangle similarly situated in , Proposition 142. Theorem. 176. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Since the homologous A are either homologous A of similar A, or else the sums of such A, the -polygons...

...respectively parallel, or respectively perpendicular, are similar. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. 367. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse...

...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 301i SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10 ; then construct...