...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...

...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...

...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...

...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. § 309 SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10 ;...

...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...

...PLANE GEOMETRY. — BOOK IV. Proposition XII 309. Draw two polygons such that they may be divided into the same number of triangles, similar, each to each, and similarly situated. How do the homologous angles of these polygons compare in size? How do the ratios of any two pairs...

...similar manner we may prove that A AED is similar to A FKI. Therefore, etc. Con. — CONVERSELY : If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the two polygons are similar. This may be readily proved, the demonstration being almost the...

...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. E' D' ED Hyp. In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE...

...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. ED Hyp, In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', D A CDE ~...

...circles. Draw the two common chords. PROPOSITION XXV. THEOREM 542. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and .similarly placed. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and...