** Square**** **** ** historicsweetsballroom.com Topical outline | Geometry synopsis | MathBits" Teacher sources **Terms that Use contact Person:** Donna Roberts

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

We will be doing two constructions of a square. The first will it is in to construct a square given the length of one side, and also the other will be to build a square enrolled in a circle.

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**STEPS:**

**1.**utilizing your straightedge, attract a referral line, if one is no provided.**2.**Copy the next of the square ~ above the recommendation line, starting at a allude labeled*A"*.**3.**construct a perpendicular at point*B"*come the line v .**4.**location your compass suggest at*B"*, and copy the side of the square top top the perpendicular . Brand the end of the segment copy as point*C*.**5.**v your compass still set at a expectancy representing*AB*, place the compass suggest at*C*and also swing one arc come the left.**6.**stop this exact same span, location the compass allude at*A"*and also swing one arc intersecting through the previous arc. Label the allude of intersection together*D*.**7.**connect points*A"*to*D, D*come*C,*and*C*to*B"*to form a square.** proof of Construction: **As a result of the building of the perpendicular in ~ *B"*, *m*∠*A"B"C* = 90º, because perpendicular lines meet to form right angles, and a right angle contains 90º. By copying the segment length of the side of the square, , we have actually *A"B" = B"C = CD = DA"*. A number having 4 congruent sides and an inner angle i beg your pardon is a right angle, is a square.

STEPS: 1. making use of your compass, attract a circle and label the center O. 2. making use of your straightedge, draw a diameter of the circle, labeling the endpoints A and also B. 3. build the perpendicular bisector of the diameter, . 4. label the points where the bisector intersects the circle as C and D. 5. connect points See more: Ultimate Guide To How Much Does A Baby Giraffe Cost ? Giraffes For Sale A to B to C come D to kind the square. |

** evidence of Construction:** is a diameter of the circle due to the fact that it passes through the center of the circle. Indigenous the construction of the perpendicular bisector of , we know that *O* is the center of (and the facility of the circle), making also a diameter that the circle. In addition,

*AO = BO = CO = DO*showing that and also bisect every other. Because the diagonals bisect every other,

*ABCD*is a parallelogram. And also since diameters that a circle room congruent, we additionally know that the diagonals of

*ABCD*are congruent and perpendicular, make

*ABCD*a square.

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