Key to Wells and Hart's Geometry; By Webster Wells ... and Walter W. Hart ... (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ... construction produces a A quite easily. 2. No A will result if Z + Z B = 180. (a) It Z A (or Z B) is 90, then AC will coincide with CD for 90-Z. 4 will then = 0. The A is a right A. (6) If Z A (or ZB) is 90, then 90-Z.4 is a negative Z..4C will then fall upon the same side of CD as line CB, producing an obtuse Z A. Ex. 37. Given 6, ma, and C. Required to construct A ABC. Construction. 1. Construct a A ACD, having as sides 6, ma, and opposite ma the Z C (following Ex. 35). 2. Extend CD its own length to B. Statement. A ABC is the required A. Discussion. The discussion is like that for Ex. 35. It is advised that only the general case of this exercise be considered. Ex. 38. Given A, tA, and ft . Required to construct A ABC. Construction. 1. Construct rt. AADE, having leg AD = ha, and hypotenuse AE = tA. 2. Draw BA, making Z BAE = Z A, meeting ED or ED extended at B. 3. Draw AC, making ZEAC = Z.A, meeting DE extended at C. Statement. A ABC is the required A. Discussion. A A cannot be made if tA h. Ex. 39. Given h the altitude to the hypotenuse AC of rt. A ABC, and a = leg BC. Required to construct A ABC. Construction. 1. Construct rt. ABDC having leg BD = h and hypotenuse BC = a. 2. Extend CD. At B, draw BA so that Z CBA = 90, meeting AC extended at A. Statement. A A BC is the required A. Discussion. A A cannot be made if a ft. Ex. 40. Given ft, the altitude to the hypotenuse AC of rt. A ABC, and acute Z A. Required to construct A ABC. Construction. 1. Construct rt. A ABD having leg BD = ft and opposite acute Z, Z BAD = given Z A (Ex. 113, Bk. II). 2. Extend AD. Construct so that ZABC =90, meeting AD extended at C. Statement. A ABCis the required A. Discussion. The construction is always possible. Ex. 41. Given A', B', and C," the mid-pts. of sides ...