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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 C and E are the midpoints of the sides they lie on, find:

  1. The perpendicular bisector of \overline{FD}.
  2. The median of \overline{FD}.
  3. The angle bisector of \angle FAD.
  4. A midsegment.
  5. An altitude.
  6. Trace \triangle 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 \triangle 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 \triangle 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 \triangle 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 x + 6 and 2x - 1. Find the range of the third side.

Texas Instruments Resources

In the CK-12 Texas Instruments Geometry FlexBook, 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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