Which of the following statements would you prove by the indirect method?
a) In
b) If alternate exterior
c) If
d) If two sides of a triangle are congruent, the two
e) The perpendicular bisector of a line segment is unique.
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Chapter 2 Solutions
Elementary Geometry for College Students
- a Is it really necessary to construct all three bisectors of the angles of a triangle to locate its incenter? b Is it really necessary to construct all three perpendicular bisectors of the sides of a triangle to locate its circumcenter?arrow_forwardFor coplanar points A,B, and C, suppose that you have used the Distance Formula to show that AB=5,BC=10, and AC=15. What can you conclude regarding points A,B, and C?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_forward
- In concave quadrilateral ABCD, the angle at A measures 40. ABD is isosceles, BC bisects ABD, and DC bisects ADB. What are the measures of ABC, ADC, and 1?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_forwardA carpenter has placed a square over an angle in such a manner that ABAC and BDCD. In the drawing, what can you conclude about the location of point D?arrow_forward
- Are quadrilaterals ABCD and EFGH congruent aif both are squares and ABEF? bif each is a rhombus and ABEF?arrow_forwardComplete the proof of the following theorem: The diagonals of an isosceles trapezoid are congruent. Given: Trapezoid ABCD; ABDC and ADBC. Prove: ACBD PROOF Statements Reasons 1_________ 2. ADCBCD 3. DCDC 4. ADCBCD 5.__________ 1.______________ 2. Base s of an isosceles trapezoid are _______. 3._________ 4.____________ 5. CPCTCarrow_forwardIn the three-dimensional figure, CAAB and BEAB. Are CAandBE parallel to each other? Compare with Exercise 6.arrow_forward
- Given: ABCD not shown with AB = 8 and BC = 6; M and N are the midpoints of sides ABandBC, respectively. Find: MNarrow_forwardIn P, whose radius has length 8in., mAB=mBC=60. Because mAC=120 chord AC is longer than either of the congruent chords AB and BC. Determine how much longer AC is than AB; that is, find the exact value and the approximate value of ACAB.arrow_forwardIn Exercises 27-30, use the definition of a parallelogram to Complete each proof. Given: WX-ZY- and s Z and Y are supplementary Prove: WXYZ is a parallelogram PROOF Statements Reasons 1. WX-ZY- 1.? 2.? 2.Given 3.? 3.If two lines are cut by a transversal so that interior s on the same side of the transversal are supplementary, these lines are 4.? 4.If both pairs of opposite side of a quadrilateral are , the quadrilateral is aarrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning