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5.7: Chapter 5 Review

Difficulty Level: At Grade Created by: CK-12
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Keywords, Theorems and Postulates

  • Midsegment
  • Midsegment Theorem
  • Perpendicular Bisector Theorem
  • Perpendicular Bisector Theorem Converse
  • Point of Concurrency
  • Circumcenter
  • Concurrency of Perpendicular Bisectors Theorem
  • Angle Bisector Theorem
  • Angle Bisector Theorem Converse
  • Incenter
  • Concurrency of Angle Bisectors Theorem
  • Median
  • Centroid
  • Concurrency of Medians Theorem
  • Altitude
  • Orthocenter
  • Theorem 5-9
  • Converse of Theorem 5-9
  • Triangle Inequality Theorem
  • SAS Inequality Theorem
  • SSS Inequality Theorem
  • Indirect Proof

Review

If \begin{align*}C\end{align*}C and \begin{align*}E\end{align*}E are the midpoints of the sides they lie on, find:

  1. The perpendicular bisector of \begin{align*}\overline{FD}\end{align*}FD¯¯¯¯¯¯¯¯.
  2. The median of \begin{align*}\overline{FD}\end{align*}FD¯¯¯¯¯¯¯¯.
  3. The angle bisector of \begin{align*}\angle FAD\end{align*}FAD.
  4. A midsegment.
  5. An altitude.
  6. Trace \begin{align*}\triangle FAD\end{align*}FAD onto a piece of paper with the perpendicular bisector. Construct another perpendicular bisector. What is the point of concurrency called? Use this information to draw the appropriate circle.
  7. Trace \begin{align*}\triangle FAD\end{align*}FAD onto a piece of paper with the angle bisector. Construct another angle bisector. What is the point of concurrency called? Use this information to draw the appropriate circle.
  8. Trace \begin{align*}\triangle FAD\end{align*}FAD onto a piece of paper with the median. Construct another median. What is the point of concurrency called? What are its properties?
  9. Trace \begin{align*}\triangle FAD\end{align*}FAD onto a piece of paper with the altitude. Construct another altitude. What is the point of concurrency called? Which points of concurrency can lie outside a triangle?
  10. A triangle has sides with length \begin{align*}x + 6\end{align*}x+6 and \begin{align*}2x - 1\end{align*}2x1. Find the range of the third side.

Texas Instruments Resources

In the CK-12 Texas Instruments Geometry FlexBook® resource, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9690.

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