...consequent). NUMERICAL PROPERTIES OF FIGURES. PROPOSITION XV. THEOREM. 334. If in a right triangte a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The perpendicular is a mean proportional between the segments of the hypotenuse. II. Each leg of the right...

...figures) whence (12) AB __ BC _ CD _ A'B' B'C' C'jy '°'''"' PROPOSITION IX.—THEOREM. • 25. 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...

...perimeters of two similar polygons have the same ratio as any two homologous sides. 334. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The perpendicular is a mean proportional between the segments of the hypotenuse. II. Each leg of the right...

...and prove the triangles ABD and ACF similar. PROPOSITION XIV. THEOREM 311. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The triangles on each side of the perpendicular are similar to the -whole triangle and to each other. II....

...and prove the triangles ABD and ACF similar. PROPOSITION XIV. THEOREM 311. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The triangles on each side of the perpendicular are similar to the whole triangle and to each other. II....

...two circles Intersect, their common chord produced bisects their common tangents. 218. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the hypotenuse, and circles inscribed in the two triangles formed, their radii are proportional to the legs of the...

...perpendicular. 70. A field has the shape of a right triangle, and the two legs are 100m and 200m respectively. A perpendicular is drawn from the vertex of the right angle to the hypotenuse. How many ars are there in each part ? 7 1 . The chord of an arc is 80cm and the chord of half the arc...

...1887. (The candidate may omit any two propositions.) 1. To inscribe a circle in a given triangle. 2. If a perpendicular is drawn from the vertex of the right angle to the hypothenuse of a right triangle: (1st.) The two triangles thus formed are similar to each other, and...

...1887. (The candidate may omit any two propositions.) 1. To inscribe a circle in a given triangle. 2. If a perpendicular is drawn from the vertex of the right angle to the hypothenuse of a right triangle: (ist.) The two triangles thus formed are similar to each other, and...

...A'E'' P = AE P ' A'E' QED PROPOSITION XVII. THEOHKM. 227. If in a right triangle a perpendicular be drawn from the vertex of the right angle to the hypotenuse: I. It divides the triangle into two right triangles ichich are similar to the whole triangle, and also...