Consider the following statement. Every parallelogram is a quadrilateral. (a) Write the converse of the given statement. O A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is not a parallelogram. (b) Write the inverse of the given statement. O A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is not a parallelogram. (c) Write the contrapositive of the given statement. A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. O If a figure is not a quadrilateral, then it is not a parallelogram.
Consider the following statement. Every parallelogram is a quadrilateral. (a) Write the converse of the given statement. O A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is not a parallelogram. (b) Write the inverse of the given statement. O A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is not a parallelogram. (c) Write the contrapositive of the given statement. A figure is a parallelogram if and only if it is a quadrilateral. If a figure is a parallelogram, then it is not a quadrilateral. If a figure is not a quadrilateral, then it is a parallelogram. If a figure is a quadrilateral, then it is a parallelogram. If a figure is not a parallelogram, then it is not a quadrilateral. O If a figure is not a quadrilateral, then it is not a parallelogram.
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
Section2.2: Indirect Proof
Problem 11E: Which of the following statements would you prove by the indirect method? a In triangle ABC, if...
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Transcribed Image Text:Consider the following statement.
Every parallelogram is a quadrilateral.
(a) Write the converse of the given statement.
A figure is a parallelogram if and only if it is a quadrilateral.
If a figure is a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is a parallelogram.
If a figure is a quadrilateral, then it is a parallelogram.
If a figure is not a parallelogram, then it is not a quadrilateral.
O If a figure is not a quadrilateral, then it is not a parallelogram.
(b) Write the inverse of the given statement.
A figure is a parallelogram if and only if it is a quadrilateral.
If a figure is a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is a parallelogram.
If a figure is a quadrilateral, then it is a parallelogram.
If a figure is not a parallelogram, then it is not a quadrilateral.
O If a figure is not a quadrilateral, then it is not a parallelogram.
(c) Write the contrapositive of the given statement.
O A figure is a parallelogram if and only if it is a quadrilateral.
If a figure is a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is a parallelogram.
If a figure is a quadrilateral, then it is a parallelogram.
If a figure is not a parallelogram, then it is not a quadrilateral.
If a figure is not a quadrilateral, then it is not a parallelogram.
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