Definition 4.6.1. Let A, B, C, and D be four points, no three of which are collinear.Suppose further that any two of the segments AB, BC, CD, and DA either have no pointin common or have only an endpoint in common. If those conditions are satisfied, thenthe points A, B, C, and D determine a quadrilateral, which we will denote by DABCD.The quadrilateral is the union of the four segments AB, BC, CD, and DA. The foursegments are called the sides of the quadrilateral and the points A, B, C, and D are calledthe vertices of the quadrilateral. The sides AB and CD are called opposite sides of thequadrilateral as are the sides BC and AD. Two quadrilaterals are congruent if there is acorrespondence between their vertices so that all four corresponding sides are congruentand all four corresponding angles are congruent.listed is important.Notice that the order in which the vertices of a quadrilateralIn general, ABCD is a different quadrilateral from DACBD. In fact, there may not evenbe a quadrilateral DAC BD since the segments AC and BD may intersect at an interiorpoint.DDeB. e12. Prove that if DABCD is a convex quadrilateral, then o(UABCD) < 360°. This is Venema exercise 4.6.1which has a small hint in the back. Your proof should clearly note where being convex is utilized in theproof

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Description: Definition 4.6.1. Let A, B, C, and D be four points, no three of which are collinear.Suppose further that any two of the segments AB, BC, CD, and DA either have no pointin common or have only an endpoint in common. If those conditions are satisfied,

Given that ABCD is a convex quadrilateral then both pairs of opposite sides are semi parallel. Now,…

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12. Prove that if DABCD is a convex quadrilateral, then o (DABCD) < 360°. This is Venema exercise 4.6.1 which has a small hint in the back. Your proof should clearly note where being convex is utilized in the proof

12. Prove that if DABCD is a convex quadrilateral, then o (DABCD) < 360°. This is Venema exercise 4.6.1 which has a small hint in the back. Your proof should clearly note where being convex is utilized in the proof

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Definition 4.6.1. Let A, B, C, and D be four points, no three of which are collinear.
Suppose further that any two of the segments AB, BC, CD, and DA either have no point
in common or have only an endpoint in common. If those conditions are satisfied, then
the points A, B, C, and D determine a quadrilateral, which we will denote by DABCD.
The quadrilateral is the union of the four segments AB, BC, CD, and DA. The four
segments are called the sides of the quadrilateral and the points A, B, C, and D are called
the vertices of the quadrilateral. The sides AB and CD are called opposite sides of the
quadrilateral as are the sides BC and AD. Two quadrilaterals are congruent if there is a
correspondence between their vertices so that all four corresponding sides are congruent
and all four corresponding angles are congruent.
listed is important.
Notice that the order in which the vertices of a quadrilateral
In general, ABCD is a different quadrilateral from DACBD. In fact, there may not even
be a quadrilateral DAC BD since the segments AC and BD may intersect at an interior
point.
D
De
B.

e
12. Prove that if DABCD is a convex quadrilateral, then o(UABCD) < 360°. This is Venema exercise 4.6.1
which has a small hint in the back. Your proof should clearly note where being convex is utilized in the
proof

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