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In exercises 27 to 33, complete a formal proof.
Given:
Prove:
(HINT: Using theorem 4.4.7, show that M is the midpoint of
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Chapter 4 Solutions
Elementary Geometry for College Students
- Circles O, P, and Q are tangent as shown at points X, Y, and Z. Being as specific as possible, explain what type of triangle PQO is if: a OX=2,PY=3,QZ=1 b OX=2,PY=3,QZ=2arrow_forwardIn Exercises 1 to 17, complete an analytic proof for each theorem. The median from the vertex of an isosceles triangle to the base is perpendicular to the base.arrow_forwardIn Exercises 11 to 14, find the distance between the two points P1 and P2. P1=0,0,0 and P2=1,2,4arrow_forward
- Given that mAC:mBC:mAB=4:3:2 in circle O: a Which arc is largest? b Which chord is longest?arrow_forwardIn ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._arrow_forwardProve the statements in Review Exercises 32 to 36 using analytic geometry. If two medians of a triangle are equal in length, then the triangle is isosceles.arrow_forward
- Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle. Exercises 34. 35arrow_forwardIn Exercises 1 to 17, complete an analytic proof for each theorem. The median of a trapezoid is parallel to the bases of the trapezoid and has a length equal to one-half the sum of the lengths of the two bases.arrow_forwardIn Exercises 27 to 30, fill in the missing reasons for each geometric proof. Given: E is the midpoint of DF Prove: DE=12(DF) Exercises 27, 28 PROOF Statements Reasons 1. E is the midpoint of DF 1. ? 2. DE=EF 2. ? 3. DE+EF=DF 3. ? 4. DE+DE=DF 4. ? 5. 2(DE)=DF 5. ? 6. DE=12(DF) 6. ?arrow_forward
- Note: Exercises preceded by an asterisk are of a more challenging nature. In the figure, which of the points E,F,G,H, and K belong to the locus of points in the plane that are at distance r from line l?arrow_forwardFor exercises 34 and 35, EFis the median of trapezoid ABCD in the figure above. Suppose that EM=7.1andMF=3.5 Find: a AB b EF c DC d Whether EF=12(AB+DC)arrow_forwardProve by the indirect method: Given: Scalene XYZ in which ZW bisects XZY point W lies on XY. Prove: ZW is not perpendicular to XYarrow_forward
- Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
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