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Square rememberingsomer.com Topical summary | Geometry outline | MathBits" Teacher sources Terms that Use call Person: Donna Roberts


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Use only your compass and straight edge when illustration a construction. No free-hand drawing!

We will certainly be doing two constructions of a square. The first will it is in to build a square offered the length of one side, and the other will it is in to build a square inscriptions in a circle.

You are watching: Construct a square with a compass


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STEPS: 1. making use of your straightedge, attract a referral line, if one is no provided. 2. Copy the next of the square top top the recommendation line, starting at a allude labeled A". 3. construct a perpendicular at suggest B" to the line with . 4. ar your compass allude at B", and also copy the side of the square onto the perpendicular
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. Brand the end of the segment copy as allude C. 5. through your compass still set at a expectancy representing AB, location the compass suggest at C and also swing an arc to the left. 6. stop this exact same span, location the compass suggest at A" and also swing one arc intersecting with the ahead arc. Brand the suggest of intersection as D. 7. affix points A" to D, D come C, and C to B" to kind a square.
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evidence of Construction: As a result of the building of the perpendicular at B", mA"B"C = 90º, since perpendicular lines satisfy to form right angles, and also a best angle has 90º. By copying the segment size of the side of the square, , we have A"B" = B"C = CD = DA". A figure having four congruent sides and also an internal angle which is a ideal angle, is a square.

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STEPS: 1. making use of your compass, attract a circle and label the facility O. 2. making use of your straightedge, attract a diameter the the circle, labeling the endpoints A and B. 3. construct the perpendicular bisector of the diameter, . 4. brand the points whereby the bisector intersects the circle together C and also D. 5.

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attach points A to B come C to D to kind the square.
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proof of Construction: is a diameter the the circle because it passes v the facility of the circle. From the construction of the perpendicular bisector that , we know that O is the center of (and the facility of the circle), do also a diameter the the circle. In addition,

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. Because both and room diameters, we have radii AO = BO = CO = DO showing that and bisect each other. Because the diagonals bisect every other, ABCD is a parallelogram. And since diameters of a circle are congruent, we additionally know that the diagonals the ABCD space congruent and also perpendicular, do ABCD a square.


Topical outline | Geometry outline | rememberingsomer.com | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts