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a) Using Sketchpad draw two point and label the O and A. Construct a regular octagon having O as center and A as one vertex. In other words, construct an octagon by center and point.
b) Open a new sketch and draw aline segment CD (don't make it too long). Construct a regular octagon having CD as one side. In other words, construct an octagon by edge.

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a) given a line segment AB and a point C above AB construct the point D on AB so that CD is perendicular to AB. We call D the foot of the perpendicular from C to AB. Prove that your construction works.

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Exercise 1.6.3, Special point of triangles:

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Exercise 1.6.3, Special point of triangles:

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Using Sketchpad, in a new sketch place a point and label it N. Construct an equilateral triangle ABC such the N is the commong incenter, orthocenter, circumcenter and centroid of equilateral traingle ABC. Describe your construction and explain why it works

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In section 1.3 a construction of an equilateral triangle starting from one side was given. This problem will expand upon those ideas.
a) draw a line segment and label its endpoint A and B. Construct a square having AB as one of its sides. Describe your construction and explain why it works
b) Draw another line segment and label it endpoints A and B. Construct a triangle ABC having a right angle at C so that the triangle remain right-angled no matter which vertex is dragged. Explain you construction and why it works. Is the effect of dragging the same at each vertex in your construction? If not why?

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(a) Consider a set of 4 point consisting of 3 vertices of a triangle and the ortrocenter of that triangle. Prove that any one point of this set is the orthocenter of the triangle formed by the remaining three points. Such a set is called an orthocentric system.

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Using sketchpad, construct each of the following figures so that the figure retain its defining property when a free point on the figure is dragged:
a) a rectangle, given perpendicular segment AB AND AC
b) a parallelogram, given two segment AB and AC with A, B, and C free points
c) a rhombus, given two segment AB and AC with AB ~ AC
d) a 30-60-90 triangle, given line segment AB as the hypotenuse of the triangle