Geometry: An Interactive Journey to Mastery

Lesson 26: Exploring Geometric Constructions

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Given that we know how to construct segments of any whole-number length and perpendicular segments, show

how to construct a line segment whose length is^1311.

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Construct a segment of length 11 and a perpendicular segment of length 13,

as shown in )LJXUH, and draw the hypotenuse of the right triangle.

Draw a segment of length 1 along the base, and construct a perpendicular

segment from its endpoint, as shown. Using matching ratios in similar

triangles, we see that 13 x 111 , showing that this perpendicular segment

has length^1311.

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x If two circles have the same radius, then any line segments that represent radii have the same length.

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ingenuity and innovation. It is often not clear how to proceed, or whether the task hoped for can even

be done. Be patient, and be kind to yourself as you try out many different possible approaches.

 Construct each of the following shapes on separate blank sheets of paper using only a straightedge and

compass. Accompany each diagram—on the reverse side of your paper—with a detailed set of instructions

that another person could follow to construct her or his own shape of the indicated type.

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Figure 26.2

Problems