i thnk i made a wrong construction :( plz correct it 

ans of b) is make an angle bisector of C . correct ?

ans of c) is perpendicular bisector of line BC


asked Jan 12 in Geometry Answers by Mac2016 Level 1 User (600 points)

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2 Answers

Best answer

Yes the bisector of angle C is correct for (b) and the perpendicular bisector of BC is correct for (c).

This is how you draw them (see picture).

Point of compasses on C and any radius smaller than BC or CD but greater than half their length, draw an arc to cut BC and CD. The blue arc is all you need for the angle bisector but I've shown the whole circle, because we can use it for part (c). Also, using the same radius draw a circle with centre B.

Now we need to draw the green arcs. Put the point of the compasses on the point on CD where the blue arc cuts. Use a radius a bit larger than before and make one of the green arcs (or you could draw the whole circle). Do the same on BC where the blue arc cuts so that the two arcs cross. Now you can draw the red angle bisector. That's part (b). 

The blue arc was part of the circle centre C. You already drew the circle centre B, so now you can draw the red perpendicular bisector where the two circles intersect. That's part (c).

Because the question is about a park, we can expect that we only need the red lines that are inside the park area.

Note that the position of A makes no difference to (b) and (c) because we are only interested in the side BC and the angle C, none of which involve A. However, to draw to scale in (a) you probably have to assume that angles D and A are right angles.

answered Jan 13 by Rod Top Rated User (486,780 points)
selected Jan 17 by Mac2016
Both of your answers are correct.

b) Draw a line from the point C bisecting the angle BCD. Any point on this line/path will be at the same distance from the line BC as the line CD.

c) Draw a line that perpindicularly bisects the line BC. Any point on this line/path will be equidistant from the points B and C.
answered Jan 12 by Fermat Level 11 User (76,040 points)

is it correct fermat ?

and what about part (a)

how to construct it ? bcoz we dont have diagonal measurment or they dont tell that D is a perpendicular line

Sorry, didn't realize ypu wanted an answer to that part.

Your construction seems to show AD and DC as perpendicular, without showing how you got them like that. With that assumption the rest of your construction looks valid,

My construction

Draw a horizontal line and using compasses, create a perpendicular bisector on it.

Draw the perpendicular bisector through the horizontal line at D, extending that line to a distance greater than 300.

Measure off a distance of 350 in the horizontal line, calling that the point C,

Set your compasses to 250 and, from D, draw an arc on the horizontal line, intersecting it at E, say.

Set your compasses to 300 and draw an arc on the vertical line, from D, intersecting it at A.

Now draw an arc, from E, cutting where the point B should be. (Using the same compasses setting of 300)

Set your compasses to 250 and draw an arc, from A, intersecting the previous arc at B.

Connect the dots.




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