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

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

**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 . 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.** evidence of Construction: **As a result of the building of the perpendicular at *B"*, *m*∠*A"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.

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. attach points See more: Spanish Numbers: How To Say 86 In Spanish Numbers: How To Count From 1 A to B come C to D to kind the square. |

** 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,

*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.

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