Given segment AB, explain how to construct a square with sides of length AB.

Question

13-10-2016
Mathematics

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Given segment AB, explain how to construct a square with sides of length AB.

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frika frika · Answer 1 · 2018-08-16T14:19:50+02:00

1. Extend the segment AB twice left and twice right. Let the point that lies left be D and the point that lies right be C. Then AD=AB=BC.

2. Draw the circles with center at points D and B and congruent radii that are greater than AB. Denote two points of their intersection as E and F.

3. Combine points E and F. The segment EF is perpendicular to the segment AB and passes through the point A.

4. Draw the circles with center at points C and A and congruent radii that are greater than AB. Denote two points of their intersection as K and L.

5. Combine points K and L. The segment KL is perpendicular to the segment AB and passes through the point B.

6. Postpone on the segment EF point X such that AX=AB and on the segment KL point Y, such that BY=AB and X and Y lie for the same side.

7. Combine points X and Y. ABYX is required square.

rahulkum rahulkum · Answer 2 · 2019-08-26T13:34:11+02:00

The square can be constructed by making perpendicular on vertex A and B. Then cut an arcs and obtain the points C and D and construct perpendicular on point C and D and get ABCD is required square.

Further Explanation:

Square is a 4 sided close figure.

Square has all sides equal and all angles are of .

The all sides of the square are perpendicular to each other.

Given:

A line segment AB.

Construction:

Steps involve in constructing a square from a line segment AB are as follows.

1. Draw a line segment AB.

2. Construct perpendicular AX at point A and then construct another perpendicular BY at point B.

3. Cut an arc on perpendicular line from A at point C that is equal to the length equal to side AB

4. Cut an arc on perpendicular line from B at point D that is equal to the length equal to side AB

5. Construct perpendicular at point C and then construct another perpendicular at point D.

6. The perpendicular intersects each other at point C and D.

The required square is ABCD is shown in figure attached.

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Construction

Keywords: square, perpendicular, , intersect, construct, line, line segment, point, right angle, sides, close figure, arc, length.