Download Schaum's Outline of Geometry (5th Edition) (Schaum's by Christopher Thomas, Barnett Rich PDF
By Christopher Thomas, Barnett Rich
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Additional info for Schaum's Outline of Geometry (5th Edition) (Schaum's Outlines Series)
Example text
4. In each part of Fig. 3-24, the congruent parts needed to prove nI Х nII are marked. Name the remaining parts that are congruent. 4) Fig. 5. In each part of Fig. 3-25, find x and y. 5) Fig. 6. Prove each of the following. BD ' AC D is midpoint of AC. To Prove: AB > BC (a) In Fig. 3-26: Given: (b) In Fig. 3-26: Given: BD is altitude to AC. BD bisects /B. To Prove: /A Х /C Fig. 6) / 1 > /2, BF > DE BF bisects /B. DE bisects /D. /B and /D are rt. To Prove: AB > CD (c) In Fig. 3-27: Given: BC > AD E is midpoint of BC.
B) All people must die. Fluffy is a cat. _____ (c) Vertical angles are congruent. (d) _____ /c and / d are vertical angles. (e) An obtuse triangle has only one obtuse angle. Conclusion (Deducted Statement) ? _____ Jan must die. _____ A square is a rectangle. A square has congruent diagonals. _____ ^ ABC has only one obtuse angle. Solutions (a) Fluffy is a domestic animal. (b) Jan is a person. (d) A rectangle has congruent diagonals. (e) ^ABC is an obtuse triangle. / c > /d. 2 Postulates (Assumptions) The entire structure of proof in geometry rests upon, or begins with, some unproved general statements called postulates.
8 Applying principles 1 and 3 In each part of Fig. 3-16, name the congruent angles that are opposite congruent sides of a triangle. Fig. 3-16 Solutions (a) Since AC > BC, /A Х /B. (b) Since AB > AC, /1 Х /2. Since BD > CD, /3 Х /4. (c) Since AB > AC > BC, /A Х /1 Х /3. Since BC > CD, /2 Х /D. (d) Since AB > BC > AC, /A Х /ACB Х /ABC. Since AE > AD > DE, /A Х /D Х /E. 9 Applying principles 2 and 4 In each part of Fig. 3-17, name the congruent sides that are opposite congruent angles of a triangle.