Isaac will be constructing congruent segments with a compass and straightedge, while Micah will be constructing a segment bisector with a compass and straightedge. Describe the similarities and differences between their construction steps.

The similarities between constructing congruent segment and constructing a segment bisector with a compass and a straightedge are as follows

1) The location of the endpoint of the congruent segment and the points on the bisector are found with the aid of the compass alone

2) The construction outline of the congruent segment and the line bisecting the segment are completed with the aid of the straight edge

The differences are;

1) The constructed congruent segment does not have to be on the original segment

2) A pair of intersecting arcs are required to construct the bisector, while only one arc is required to construct the congruent segment

3) The compass needle is placed at both end points when constructing a segment bisector while the compass needle is placed only at the defined start point when constructing congruent segments

Step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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