Christopher Thomas, Barnett Rich's Schaum's Outline of Geometry (5th Edition) (Schaum's PDF

By Christopher Thomas, Barnett Rich

ISBN-10: 0071795413

ISBN-13: 9780071795418

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Extra resources for Schaum's Outline of Geometry (5th Edition) (Schaum's Outlines Series)

Example text

E) In Fig. 3-23(c) by SSS. (f) In Fig. 3-23(c) by SAS. 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.

Principle 3 is a corollary of Principle 1. A corollary of a theorem is another theorem whose statement and proof follow readily from the theorem. Fig. 3-14 40 CHAPTER 3 Congruent Triangles PRINCIPLE 4: An equiangular triangle is equilateral. Thus in nABC in Fig. 3-15, if /A Х /B Х /C, then AB > BC > CA. Principle 4 is the converse of Principle 3 and a corollary of Principle 2. Fig. 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.

Opposite BC and AD, /1 Х /4. Opposite common side BD, /A Х /C. (c) Opposite AE and ED, /2 Х /3. Opposite BE and EC, /1 Х /4. Opposite /5 and /6, AB > CD. 5 CHAPTER 3 Congruent Triangles Applying algebra to congruent triangles In each part of Fig. 3-11, find x and y. Fig. 3-11 Solutions (a) Since nI Х nII, by SSS, corresponding angles are congruent. Hence, 2x ϭ 24 or x ϭ 12, and 3y ϭ 60 or y ϭ 20. (b) Since nI Х nII, by SSS, corresponding angles are congruent. Hence, x ϩ 20 ϭ 26 or x ϭ 6, and y Ϫ 5 ϭ 42 or y ϭ 47.

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Schaum's Outline of Geometry (5th Edition) (Schaum's Outlines Series) by Christopher Thomas, Barnett Rich


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