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3. Given four points, A, B, C, and D, no three of which are collinear and such that any pair of the segments AB, BC, CD, and DA cither have no point in common or have only an endpoint in common. We can then define the quadrilateral DABCD to consist of the four segments men- tioned, which are called its sides, the four points being called its vertices; see Figure 1.20. (Notc that the order in which the letters are written is cssential. For example, DABCD may not denote a quadrilateral, be- cause, for example, AB might cross CD. If DABCD did denote a quadrilateral, it would not denote the same one as DACDB. Which permutations of the four letters A, B, C, and D do denote the same quadrilateral as DABCD?) Using this definition, define the following notions: (a) The angles of DABCD. (b) Adjacent sides of DABCD. (c) Opposite sides of DABCD. (d) The diagonals of DABCD. (e) A parallelogram. (Use the word "parallel.")

3. Given four points, A, B, C, and D, no three of which are collinear and such that any pair of the segments AB, BC, CD, and DA cither have no point in common or have only an endpoint in common. We can then define the quadrilateral DABCD to consist of the four segments men- tioned, which are called its sides, the four points being called its vertices; see Figure 1.20. (Notc that the order in which the letters are written is cssential. For example, DABCD may not denote a quadrilateral, be- cause, for example, AB might cross CD. If DABCD did denote a quadrilateral, it would not denote the same one as DACDB. Which permutations of the four letters A, B, C, and D do denote the same quadrilateral as DABCD?) Using this definition, define the following notions: (a) The angles of DABCD. (b) Adjacent sides of DABCD. (c) Opposite sides of DABCD. (d) The diagonals of DABCD. (e) A parallelogram. (Use the word "parallel.")

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.5: Convex Polygons
Problem 41E
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3. Given four points, A, B, C, and D, no three of which are collinear and such that any pair of the segments AB, BC, CD, and DA cither have no point in common or have only an endpoint in common. We can then define the quadrilateral DABCD to consist of thc four segments men- tioned, which are called its sides, the four points being called its vertices; see Figure 1.20. (Note that the order in which the letters are written is essential. For example, DABCD may not denote a quadrilateral, bc- cause, for example, AB mighr cross CD. If DABCD did denote a quadrilateral, it would not denote the same one as DACDB. Which permutations of the four letters A, B, C, and D do denote the same quadrilateral as DABCD?) Using this definition, define the following notions: (a) The angles of DABCD. (b) Adjacent sides of DABCD. (c) Opposite sides of DABCD. (d) The diagonals of DABCD. (e) A parallelogram. (Use the word "parallel.") B
Transcribed Image Text:3. Given four points, A, B, C, and D, no three of which are collinear and such that any pair of the segments AB, BC, CD, and DA cither have no point in common or have only an endpoint in common. We can then define the quadrilateral DABCD to consist of thc four segments men- tioned, which are called its sides, the four points being called its vertices; see Figure 1.20. (Note that the order in which the letters are written is essential. For example, DABCD may not denote a quadrilateral, bc- cause, for example, AB mighr cross CD. If DABCD did denote a quadrilateral, it would not denote the same one as DACDB. Which permutations of the four letters A, B, C, and D do denote the same quadrilateral as DABCD?) Using this definition, define the following notions: (a) The angles of DABCD. (b) Adjacent sides of DABCD. (c) Opposite sides of DABCD. (d) The diagonals of DABCD. (e) A parallelogram. (Use the word "parallel.") B
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