Chapter 3 Geometry Homework Answers

Sec 3.1 1-2) See diagrams. 3-8) See diagrams (page 768 in Teacher’s Edition). See description and diagram. a = 50, b = 130, c = 50, d = 130, e = 50, f = 50, g = 130, h = 130, k = 155, l = 90, m = 115, n = 65 West Answers to 12 are in degrees.

Sec 3.2 1-5) See diagrams (pages 768-769 in Teacher’s Edition). See diagram. The perpendicular bisectors all intersect in one point. See diagram. The medians all intersect in one point. See diagram. GH appears to be parallel to EF and its length is half the length of EF. F E B A D C

Sec 3.3 1-5) See diagrams (pages 769-770 in Teacher’s Edition).

Sec 3.4 D F A C E 6-12) See diagrams (page 770 in Teacher’s Edition). If a point is equally distant from the sides of an angle, then it is on the bisector of an angle. This is true for points in the same planes as the angle. STOP See diagram. No, the triangles don’t look the same.

Sec 3.5 1-2, 4-6) See diagrams (pages 770-771 in Teacher’s Edition). Draw a line and construct ML perpendicular to it. Swing an arc from point M to point G so that MG = RA. From point G, swing an arc to construct RG. Finish the parallelogram by swinging an arc of length RA from R and swinging an arc of length GR from M. There is only one possible parallelogram. ‹ 1 ≈ ‹ S, ‹ 2 ≈ ‹ U; AIA a = 72, b = 108, c = 108, d = 108, e = 72, f = 108, g = 108, h = 72, j = 90, k = 18, l = 90, m = 54, n = 62, p = 62, q = 59, r = 118 12-14) See diagrams. Answers to 11 are in degrees.

Using Your Algebra Skills 3:Slopes of Parallel and Perpendicular Lines a. Yes, the diagonals are perpendicular. Slope OE = 1; slope VR = -1. Neither b. Midpoint VR = midpoint OE = (-2, 4). The diagonals of OVER bisect each other. Parallel c. OVER appears to be a rhombus because the sides are parallel and appear to be the same length. Ordinary; no two slopes are the same, so no sides are parallel although TE is perpendicular to EM because their slopes are negative reciprocals. a. Both slopes equal ½. Ordinary, for the same reason as in Exercise 7- none of the sides are quite parallel. b. The segments are not parallel because they are coincident. Trapezoid: KC is parallel to RO c. Distinct a. Slope HA = slope ND = 1/6; slope HD = slope NA = -6. Quadrilateral HAND is a rectangle because opposite sides are parallel and adjacent sides are perpendicular. b. Midpoint HN = midpoint AD = (1/2, 3). The diagonals of a rectangle bisect each other.

Sec 3.6 1-7) See diagrams (page 771 in Teacher’s Edition). 4) See diagram. Yes, students’ constructions must be either larger or smaller than the triangle in the book. See diagram.

Sec 3.7 See diagram. Incenter E A See diagram. Circumcenter B Circumcenter. Find the perpendicular bisectors of two of the sides of the triangle formed by the classes. Locate the pie table where these two lines intersect. D See diagram. The circumcenter of a right triangle lies on the midpoint of the hypotenuse. The orthocenter of a right triangle lies on the vertex of the right angle. See diagram. The midsegment appears parallel to side MA and half the length.

Sec 3.8 The center of gravity is the centroid. She needs to locate the incenter to create the largest circle within the triangle. AM = 20, SM = 7, TM = 14, UM = 8 BG = 24, IG = 12 RH = 42, TE = 45 See diagram. The points of concurrency are the same point or equilateral triangles because the segments are the same. Circumcenter a = 128, b = 52, c = 128, d = 128, e = 52, f = 128, g = 52, h = 38, k = 52, m = 38, n = 71, p = 38 1710 greetings Answers to 14 are in degrees.

Ch 3 Review False; a geometric construction uses a straightedge and a compass. J C False; a side connects two consecutive vertices. True False; see diagram. B False; the lines can’t be a given distance from a segment because the segment has a finite length and the lines are infinite. False; an isosceles triangle has two congruent sides. False; any non-acute triangle is a counterexample. False; possible explanation: The orthocenter is the point of intersection of the three altitudes. False; orthocenter does not always lie inside the triangle. False; any linear of angles is a counterexample. A False; each side is adjacent to one congruent side and one noncongruent side, so two consecutive sides may not be congruent. B or K I H G False; the measure of an arc is equal to the measure of its central angle. D

Ch 3 Review (cont’d) False; TD = 2DR False; a radius is not a chord. True False; inductive reasoning is the process of observing data, recognizing patterns, and making generalizations about those patterns. Paradox a. ‹ 2 and ‹ 6 or ‹ 3 and ‹ 5 b. ‹ 1 and ‹ 5 c. 138° a. Yes b. If the month has 31 days, then the month is October. c. No