17. ABC is a right-angled triangle (C=903), and CD is drawn perpendicular to AB. (1) Prove that triangles CAD and BAC are equiangular; also CBD and ABC equiangular. 18. The school expenditures for certain cities, in 1901-2, being as follows: San Francisco, $1331541; St. Louis, $1636575; Boston, $4007264; Philadelphia, $4223277; Chicago, $8511019; New York, $23013600; construct equilateral triangles, with one angle common, whose areas shall proportionately and approximately represent these expenditures, the side of the first triangle being 12 millimetres. 19. What will be the sides of the triangles if their perimeters are to represent the expenditures, the side of the first being again 12 milli metres ? 20. Construct two triangles, the sides of one being twice the sides of the other, and ascertain the following: (1) The ratio of perpendiculars from corresponding angles on opposite sides. (2) The ratio of corresponding segments (of sides) made by feet of perpendiculars. (3) The ratio of lines from corresponding angles to bisections of opposite sides. |