# 5.7: Chapter 5 Review

Difficulty Level:

**At Grade**Created by: CK-12Turn In

**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:

- The perpendicular bisector of \begin{align*}\overline{FD}\end{align*}.
- The median of \begin{align*}\overline{FD}\end{align*}.
- The angle bisector of \begin{align*}\angle FAD\end{align*}.
- A midsegment.
- An altitude.
- 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.
- 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.
- 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?
- 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?
- 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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Tags:

altitudes
angle bisector
angle bisectors
(17 more)
CK.MAT.ENG.SE.1.Geometry-Basic.5
CK.MAT.ENG.SE.2.Geometry.5
concurrency
indirect proof
inscribe
medians
mid-segment
Midsegment Theorem
midsegments
perpendicular bisector
perpendicular bisectors
proof
Segments
sides of triangles
triangle inequalities
Triangle Inequality Theorem
triangles

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Date Created:

Jul 24, 2013
Last Modified:

Sep 21, 2015
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