Using ruler and a pair of compass only
a. Construct square ABCD with |AB|=7cm
b. Construct a point Equidistant from |BA| and |BC|
c. Construct a point equidistant from |DA| and |AB|
d. Label the point of intersection of two bisectors as M and draw a circle of radius 0.1metres and M as the centre.
e. Measure angle MAB
so do it
to draw a square draw two lines at right angles first. The rest is easy.
To draw a right angle draw a line, any length from some point x to another point
set your compass at any length greater than half the length x y
swing the compass from x and from y both sides of line x y
The compass arcs hit at points on each side of the line, same distance from x as from y
the line between those arc intersections is the perpendicular bisector
now draw the four sides of equal length.
I think that pretty well settles the rest as well.
To construct a square ABCD with side |AB| = 7cm using a ruler and a pair of compass, follow these steps:
a. Draw a line segment AB of length 7cm using a ruler.
b. Place the compass at point A and draw an arc with a radius of 7cm. This arc should intersect the line segment AB. Label the intersection point as C.
c. Using the same compass setting, place the compass at point B and draw an arc to intersect the line segment AB. Label the intersection point as D.
d. Finally, connect the points C and D to complete the square ABCD.
Now, moving on to the next part:
b. To construct a point equidistant from |BA| and |BC|, follow these steps:
a. Take the compass and place the sharp end on point B.
b. Adjust the compass to a width slightly more than half the length of |BA|.
c. Draw two arcs on either side of the line segment BA. These arcs should intersect the line segment BA at points E and F.
d. Without changing the compass width, place the sharp end on point C.
e. Draw two arcs on either side of the line segment BC. These arcs should intersect the line segment BC at points G and H.
f. Now, draw a straight line connecting points F and G. The intersection of this line with line segment BA will give you a point equidistant from |BA| and |BC|. Label this point as P.
c. To construct a point equidistant from |DA| and |AB|, follow these steps:
a. Place the sharp end of the compass on point D.
b. Adjust the compass width to a length slightly more than half the length of |DA|.
c. Draw two arcs on either side of the line segment DA. These arcs should intersect the line segment DA at points K and L.
d. Without changing the compass width, place the sharp end on point A.
e. Draw two arcs on either side of the line segment AB. These arcs should intersect the line segment AB at points M and N.
f. Now, draw a straight line connecting points L and M. The intersection of this line with line segment DA will give you a point equidistant from |DA| and |AB|. Label this point as Q.
d. To find the point of intersection of two bisectors, B and C, and draw a circle with radius 0.1 meters (or any other unit) and M as the center, follow these steps:
a. Draw the bisector of angle B using a compass and ruler. Label the point where the bisector intersects line segment CD as X.
b. Draw the bisector of angle C using a compass and ruler. Label the point where the bisector intersects line segment AD as Y.
c. Using the compass, place the sharp end at point M and draw a circle with a radius of 0.1 meters.
e. Once you have constructed the circle with M as the center and a radius of 0.1 meters, you can measure the angle MAB using a protractor. Place the protractor on line segment AB with one side coinciding with AB, and measure the angle formed with the other side coinciding with line segment AM. The measurement will give you the angle MAB.