Question

Jason uses the following steps to construct a perpendicular through a point C on a line segment.

Step 1: From point C, draw an arc intersecting the line segment in points A and B.
Step 2: Draw two arcs from point A, one above and the other below the line segment.
Step 3: Using slightly more compass width, draw two arcs from point B, above and below the line segment.
Step 4: Label the point of intersection of the arcs above the line segment as D and below the line as E.
Step 5: Using a straightedge, join points D and E.

Answer 1

Part A: Which is the first incorrect step?
Part B: Using complete sentences, explain your answer for Part A.
Part C: Explain why a compass works for the construction done by Jason.

Answer 2

3 is incorrect right? width of compass should be same?

Answer 3

Actually, #2 is wrong. From A, you have to get that radius AND the radius in step 3 ( from point b) the same length, and BOTH have to be equal and bigger than the very first arc.

Answer 4

So, if you make the compass bigger in step 2, draw from A, go to step 3 and keep the compass the same size for the B arcs, you'll have your perpendicular drawn from the intersecting points above and below C. Math is cool.

Answer 5

slightly confusing but i think i get it..

Answer 6

@imron07 @hartnn you guys have a second opinion?

Answer 7

Don't let it confuse. We can go over it. It works because the triangles ACD is congruent to BCD. All corresponding sides are equal. So the angle ACD = BCD where they add to 180, so they are each 90, so perpendicular. Same for the lower 2 sets of triangles.

Answer 8

Like this?