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Consider the following steps for a construction. Steps 1. Using your compass, draw a circle and label the center O. 2. Using your straightedge, draw a diameter of the circle, labeling the endpoints A and B. 3. Construct the perpendicular bisector of the diameter constructed in step 2. 4. Label the points where the bisector intersects the circle as C and D. S.Connect points A to B to C to D. Which of the following BEST describes by using the construction what type of quadrilateral is created in step 5? The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a square are congruent, perpendicular bisectors. The quadrilateral is a rhombus, but not a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a rhombus are congruent, perpendicular bisectors. The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. These diagonals are perpendicular bisectors, but are not congruent. The diagonals of a square are non-congruent, perpendicular bisectors.

Consider the following steps for a construction. Steps 1. Using your compass, draw a circle and label the center O. 2. Using your straightedge, draw a diameter of the circle, labeling the endpoints A and B. 3. Construct the perpendicular bisector of the diameter constructed in step 2. 4. Label the points where the bisector intersects the circle as C and D. S.Connect points A to B to C to D. Which of the following BEST describes by using the construction what type of quadrilateral is created in step 5? The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a square are congruent, perpendicular bisectors. The quadrilateral is a rhombus, but not a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a rhombus are congruent, perpendicular bisectors. The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. These diagonals are perpendicular bisectors, but are not congruent. The diagonals of a square are non-congruent, perpendicular bisectors.

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.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Understanding Rhombus Properties** The quadrilateral discussed here is a rhombus, which is distinct from a square. When you construct the perpendicular bisector of the diameter in a specific step, it generates two diagonals of the inscribed quadrilateral. These diagonals are perpendicular bisectors, meaning they intersect at 90 degrees. However, they are not congruent, or in other words, not equal in length. This characteristic is a defining feature of a rhombus: its diagonals are non-congruent, perpendicular bisectors.
Transcribed Image Text:**Understanding Rhombus Properties** The quadrilateral discussed here is a rhombus, which is distinct from a square. When you construct the perpendicular bisector of the diameter in a specific step, it generates two diagonals of the inscribed quadrilateral. These diagonals are perpendicular bisectors, meaning they intersect at 90 degrees. However, they are not congruent, or in other words, not equal in length. This characteristic is a defining feature of a rhombus: its diagonals are non-congruent, perpendicular bisectors.
``` Consider the following steps for a construction. Steps: 1. Using your compass, draw a circle and label the center O. 2. Using your straightedge, draw a diameter of the circle, labeling the endpoints A and B. 3. Construct the perpendicular bisector of the diameter constructed in step 2. 4. Label the points where the bisector intersects the circle as C and D. 5. Connect points A to B to C to D. Which of the following BEST describes by using the construction what type of quadrilateral is created in step 5? A. The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a square are congruent, perpendicular bisectors. B. The quadrilateral is a rhombus, but not a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a rhombus are congruent, perpendicular bisectors. C. The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. These diagonals are perpendicular bisectors, but are not congruent. The diagonals of a square are non-congruent, perpendicular bisectors. ``` There is no graph or diagram accompanying the text. The steps describe the geometric construction of a quadrilateral inscribed in a circle. The question asks which type of quadrilateral is formed following the steps.
Transcribed Image Text:``` Consider the following steps for a construction. Steps: 1. Using your compass, draw a circle and label the center O. 2. Using your straightedge, draw a diameter of the circle, labeling the endpoints A and B. 3. Construct the perpendicular bisector of the diameter constructed in step 2. 4. Label the points where the bisector intersects the circle as C and D. 5. Connect points A to B to C to D. Which of the following BEST describes by using the construction what type of quadrilateral is created in step 5? A. The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a square are congruent, perpendicular bisectors. B. The quadrilateral is a rhombus, but not a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. The diagonals are congruent to each other and are also perpendicular bisectors. The diagonals of a rhombus are congruent, perpendicular bisectors. C. The quadrilateral is a square. By constructing the perpendicular bisector of the diameter in step 3, this creates two diagonals of the inscribed quadrilateral. These diagonals are perpendicular bisectors, but are not congruent. The diagonals of a square are non-congruent, perpendicular bisectors. ``` There is no graph or diagram accompanying the text. The steps describe the geometric construction of a quadrilateral inscribed in a circle. The question asks which type of quadrilateral is formed following the steps.
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