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5.6: Chapter 5 Review

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

Midsegments in Triangles

  • Midsegment
  • Midsegment Theorem

Perpendicular Bisectors and Angle Bisectors in Triangles

  • Perpendicular Bisector Theorem
  • Perpendicular Bisector Theorem Converse
  • Inscribe
  • Circumscribe
  • Angle Bisector Theorem
  • Angle Bisector Theorem Converse

Medians and Altitudes in Triangles

  • Median
  • Centroid
  • Median Theorem
  • Altitude

Inequalities in Triangles

  • Theorem 5-9
  • Converse of Theorem 5-9
  • Triangle Inequality Theorem
  • SAS Inequality Theorem
  • SSS Inequality Theorem

Extension: Indirect Proof


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

  1. The perpendicular bisector of \begin{align*}\overline{FD}\end{align*}.
  2. The median of \begin{align*}\overline{FD}\end{align*}.
  3. The angle bisector of \begin{align*}\angle FAD\end{align*}.
  4. A midsegment.
  5. An altitude.
  6. A triangle has sides with length \begin{align*}x + 6\end{align*} and \begin{align*}2x - 1\end{align*}. Find the range of the third side.

Fill in the blanks.

  1. A midsegment connects the __________ of two sides of a triangle.
  2. The height of a triangle is also called the __________.
  3. The point of intersection for all the medians of a triangle is the __________.
  4. The longest side is opposite the __________ angle in a triangle.
  5. A point on the __________ bisector is __________ to the endpoints.
  6. A point on the __________ bisector is __________ to the sides.
  7. A circle is __________ when it touches all the sides of a triangle.
  8. An __________ proof is also called a proof by contradiction.
  9. For \begin{align*}\triangle ABC\end{align*} and \begin{align*}\triangle DEF: \ AB = DE, \ BC = EF\end{align*}, and \begin{align*}m \angle B > m \angle E\end{align*}, then __________.

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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