...divided into equal parts at the points I, K, L. PROPOSITION XXVII. — THEOREM. 269. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothe«tt.se, the triangle will be divided into two triangles similar to the given triangle and to...

...o\if Kai In a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of the perpendicular are similar to the whole and to Statement. — Let ABC be a right-angled triangle, having the right angle ABC, and from the...

...parallel chords in a circle, is a point in the diameter which is perpendicular to the chords. O. 4. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle, (1) the triangles thus formed are similar to each other and to the whole triangle,...

...in the ratio of similitude of the polygons (40). 10 APPLICATIONS. PROPOSITION XIII.— THEOREM. 44. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a rigid triangle : 1st. The two triangles thus formed are similar to each other and to the whole...

...: A2 : «2 + b2. But A8 = a2 + b2 (90), consequently, S = s + «i. THEOREM. 120. In a right-angled triangle if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the square or any other figure on the hypothenuse is to the square or other similar figure...

...in the ratio of similitude of the polygons (40). 10 APPLICATIONS. PROPOSIT1ON XIII.— THEOKEM. 44. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle : 1st. The two triangles thus formed are similar to each other and to the whole...

...homologous. Thus, DE is homologous with AB, DF with AC, and EF with BC. THEOREM XVII. 210i In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle and to each...

...triangles AC :AB = AB:AD And since ABC and BCD are similar AC: CB=CB:CD that is, if in a right triangle a perpendicular is drawn from, the vertex of the right angle to the hypothenuse, either side about the right angle is a mean proportional between the whole hypothenuse...

...triangles AC :AB — AB :AD And since ABC and BCD are similar AC : CB=CB:CD that is, if in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypothenuse, either side about the right angle is a mean proportional between the whole hypothenuse...

...Thus, DE is homologous with AB, DF with AC, and EF with £ C. THEOREM XVII. 210. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle and to each...