...into equal parts at the points 7J K, L. PROPOSITION XXIII. THEOEEM. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse. \st. The triangles on each side of the perpendicular are similar to the whole triangle, and to each...

...into equal parts at the points I, K, L. PROPOSITION XXIII. THEOREM. In a right•angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse. 1st. The triangles on each side of the jxrpendicular are similar to the given triangle, and to each...

...into equal parts at the points I, K, L. PROPOSITION XXIII. THEOREM. In a right•angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse. 1st. The triangles on each side of the perpendicular are similat to the given triangle, and to each...

...(he vertices of the triangle ; then AN x BL X CM = AM X CL x BN. 14. In a right angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, 1st. The triangles formed are similar to each other and to the whole triangle. 2d. Either side about...

...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 hypothenuse, the triangle will be divided into two triangles similar to the given triangle atul to each other. In...

...vertices of the triangle ; the» AN x HI, x CM = AM x CL x BN. 14.' In a right angled triangle, if л perpendicular is drawn from the vertex of the right angle to the hypothenuse 1st. The triangles formed are similar to each other and to the whole triangle. 2d. Either side about...

...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...

...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...

...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...

...+ 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 on either...