SOLUTION: 1) Given a segment x long construct a rhombus, whose perimeter is x and having one pair of opposite angles that are 45 degree. tell me the steps to do it. PLEASE help me about this

Question 202977This question is from textbook Discovering geometry an investigative approach
: 1) Given a segment x long construct a rhombus, whose perimeter is x and having one pair of opposite angles that are 45 degree. tell me the steps to do it. PLEASE help me about this problem. its due tomorrow(July 14th). Please help me...... This question is from textbook Discovering geometry an investigative approach

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
using a compass and a straight edge

a rhombus has four equal sides
bisect the segment (x), and then bisect one of the halves ___ this is the length of one of the sides of the rhombus (x/4)

construct a set of perpendicular lines (like coordinate axes)

bisect a right angle (formed by the axes) ___ this angle is 45� (half of 90�)

set the compass opening to the x/4 distance ___ point on one end of x/4 and scribe on the other end

set the point of the compass at the vertex of the 45� angle

make an arc through the two arms of the angle ___ this makes two sides x/4 long, at a 45� angle

set the compass point at the end of each x/4 side and strike an arc
where the two arcs cross is the other corner of the rhombus
draw the sides from the ends of the first set of sides to the intersection of the arcs
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