Which formula would you use to establish each of the following claims?
a) The coordinates of
b)
c)
d) The length of
Trapezoid
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Elementary Geometry For College Students, 7e
- 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_forwardNote: Exercises preceded by an asterisk are of a more challenging nature. In the figure, which of the points A,B,C,D, and E belong to the locus of points in the plane that are at distance r from point P?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
- In Exercises 15 to 20, use that fact that r2+h2=l2 in a right circular cone Theorem 9.3.6. Find the length of the slant height l of a right circular cone with r=5.2 ft and h=3.9 ft.arrow_forwardThe center of a circle of radius 2 in. is at a distance of 10 in. from the center of a circle of radius length 3 in. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.arrow_forwardFor compactness, the drop-down wheels of a stretcher or gurney are folded under it as shown. In order for the boards upper surface to be parallel to the ground when the wheels are dropped, what relationship must exist between AB and CD?arrow_forward
- For Exercise 31 and 32, X is the midpoint of VT and Y is the midpoint of TS. See the theorem in Exercise 30. If ARSTV=48cm2, find ARYTX. Exercises 31, 32arrow_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_forwardGiven: Isosceles ABE with AEBE; also, D and C are midpoints of AE and BE, respectively. Prove: ABCD is an isosceles trapezoid. Exercises 17, 18arrow_forward
- Consider regular pentagon RSTVQ not shown. Given that diagonals QT and VR intersect at point F, show that VFFR=TFFQ.arrow_forwardIn Exercises 1 to 17, complete an analytic proof for each theorem. The diagonals of an isosceles trapezoid are equal in length.arrow_forwardComplete 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.arrow_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