# 5.7: Chapter 5 Review

Difficulty Level: At Grade Created by: CK-12

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*} 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. Trace \begin{align*}\triangle FAD\end{align*} 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*} 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*} 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*} 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*} and \begin{align*}2x - 1\end{align*}. 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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