# ssrs barcode font Parallelograms, Trapezoids, Medians, and Midpoints in Objective-C Generating QR Code in Objective-C Parallelograms, Trapezoids, Medians, and Midpoints

CHAPTER 5 Parallelograms, Trapezoids, Medians, and Midpoints
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5.16. Find x and y in each part of Fig. 5-39.
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Fig. 5-39
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5.17. In a right triangle (a) Find the length of the median to a hypotenuse whose length is 45. (b) Find the length of the hypotenuse if the length of its median is 35. 5.18. If the medians of nABC meet in D (a) Find the length of the median whose shorter segment is 7. (b) Find the length of the median whose longer segment is 20. (c) Find the length of the shorter segment of the median of length 42. (d) Find the length of the longer segment of the median of length 39. 5.19. Prove each of the following:
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(a) If the midpoints of the sides of a rhombus are joined in order, the quadrilateral formed is a rectangle. (b) If the midpoints of the sides of a square are joined in order, the quadrilateral formed is a square. (c) In nABC, let M, P, and Q be the midpoints of AB, BC, and AC, respectively. Prove that QMPC is a parallelogram. (d) In right nABC, m/C 90 . If Q, M, and P are the midpoints of AC, AB, and BC, respectively, prove that QMPC is a rectangle.
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Circles
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6.1 The Circle; Circle Relationships
The following terms are associated with the circle. Although some have been defined previously, they are repeated here for ready reference. A circle is the set of all points in a plane that are at the same distance from a fixed point called the cens ter. The symbol for circle is }; for circles ~. The circumference of a circle is the distance around the circle. It contains 360 . A radius of a circle is a line segment joining the center to a point on the circle. Note: Since all radii of a given circle have the same length, we may at times use the word radius to mean the number that is the length of the radius. A central angle is an angle formed by two radii. An arc is a continuous part of a circle. The symbol for arc is C. A semicircle is an arc measuring one-half the circumference of a circle. A minor arc is an arc that is less than a semicircle. A major arc is an arc that is greater than a semicircle.
Fig. 6-1
Fig. 6-2
Thus in Fig. 6-1, BC is a minor arc and BAC is a major arc. Three letters are needed to indicate a major arc.
To intercept an arc is to cut off the arc.
Thus in Fig. 6-1, jBAC and jBOC intercept BC.
A chord of a circle is a line segment joining two points of the circumference.
Thus in Fig. 6-2, AB is a chord.
A diameter of a circle is a chord through the center. A secant of a circle is a line that intersects the circle at two points. A tangent of a circle is a line that touches the circle at one and only one point no matter how far produced.
CHAPTER 6 Circles
Thus, CD is a diameter of circle O in Fig. 6-2, EF is a secant, and GH is a tangent to the circle at P. P is the point of contact or the point of tangency.
An inscribed polygon is a polygon all of whose sides are chords of a circle. A circumscribed circle is a circle passing through each vertex of a polygon.
Fig. 6-3 Thus ^ ABD, ^ BCD, and quadrilateral ABCD are inscribed polygons of circle O in Fig. 6-3. Circle O is a circumscribed circle of quadrilateral ABCD.
A circumscribed polygon is a polygon all of whose sides are tangents to a circle. An inscribed circle is a circle to which all the sides of a polygon are tangents.
Thus, ^ ABC is a circumscribed polygon of circle O in Fig. 6-4. Circle O is an inscribed circle of ^ ABC.