** Square**** **** ** thedailysplash.tv Topical summary | Geometry synopsis | MathBits" Teacher resources **Terms that Use call Person:** Donna Roberts

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

We will certainly be doing 2 constructions the a square. The first will it is in to construct a square offered the length of one side, and the other will be to construct a square inscribed in a circle.

You are watching: Given ab explain how to construct a square with sides of length ab

**STEPS:**

**1.**using your straightedge, attract a referral line, if one is not provided.**2.**Copy the side of the square ~ above the recommendation line, beginning at a point labeled*A"*.**3.**build a perpendicular at allude*B"*come the line with .**4.**location your compass suggest at*B"*, and copy the next of the square ~ above the perpendicular . Brand the end of the segment copy as point*C*.**5.**through your compass still set at a expectations representing*AB*, location the compass allude at*C*and also swing an arc come the left.**6.**stop this exact same span, place the compass allude at*A"*and swing an arc intersecting through the previous arc. Label the point of intersection as*D*.**7.**attach points*A"*to*D, D*come*C,*and*C*to*B"*to type a square.** proof of Construction: **As a an outcome of the building of the perpendicular at *B"*, *m*∠*A"B"C* = 90º, since perpendicular lines accomplish to form right angles, and also a ideal angle has 90º. By copy the segment size of the next of the square, , we have *A"B" = B"C = CD = DA"*. A number having 4 congruent sides and an internal angle i m sorry is a right angle, is a square.

STEPS: 1. making use of your compass, draw a circle and also label the facility O. 2. utilizing your straightedge, draw a diameter the the circle, labeling the endpoints A and also B. 3. build the perpendicular bisector the the diameter, . 4. label the points where the bisector intersects the circle together C and D. 5. affix points See more: Reaction New Years Eve 2017, Ring In 2017 With Gucci Mane, Anderson A to B come C to D to form the square. |

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

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

*ABCD*is a parallelogram. And also since diameters the a circle space congruent, we likewise know the the diagonals that

*ABCD*are congruent and also perpendicular, do

*ABCD*a square.

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