Lesson 1

Build It

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Problem 1

Here is a diagram of a straightedge and compass construction. \(C\) is the center of one circle, and \(B\) is the center of the other. Explain why the length of segment \(BD\) is the same as the length of segment \(AB\).

 
Two circles intersect. Smaller circle center B. Larger circle center C, goes through center B and intersects smaller circle at points A and D. Segments AB and BD are drawn.
 

Solution

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Problem 2

Clare used a compass to make a circle with radius the same length as segment \(AB\). She labeled the center \(C\). Which statement is true?

Line segments AB and CF are drawn with the same length. Circle with center C passes through point F. Point D lies inside the circle and point E lies outside the circle. Points C, F, and E are collinear.
A:

\(AB > CD\)

B:

\(AB = CD\)

C:

\(AB > CE\)

D:

\(AB = CE\)

Solution

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Problem 3

The diagram was constructed with straightedge and compass tools. Points \(A\), \(B\), \(C\), \(D\), and \(E\) are all on line segment \(CD\). Name a line segment that is half the length of \(CD\). Explain how you know.

Three congruent circles, each pass through the others center at points A, B, and E, and intersect line segment with the endpoints C and D. Points C, A, B, E, and D are collinear and equidistant.

Solution

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Problem 4

This diagram was constructed with straightedge and compass tools. \(A\) is the center of one circle, and \(C\) is the center of the other.

Two circles intersecting.
  1. The 2 circles intersect at point \(B\).  Label the other intersection point \(E\).
  2. How does the length of segment \(CE\) compare to the length of segment \(AD\)?

Solution

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