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# 5.6: Chapter 5 Review

Difficulty Level: At Grade Created by: CK-12

## 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

## Review

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

1. The perpendicular bisector of FD¯¯¯¯¯¯¯¯\begin{align*}\overline{FD}\end{align*}.
2. The median of FD¯¯¯¯¯¯¯¯\begin{align*}\overline{FD}\end{align*}.
3. The angle bisector of FAD\begin{align*}\angle FAD\end{align*}.
4. A midsegment.
5. An altitude.
6. A triangle has sides with length x+6\begin{align*}x + 6\end{align*} and 2x1\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 ABC\begin{align*}\triangle ABC\end{align*} and DEF: AB=DE, BC=EF\begin{align*}\triangle DEF: \ AB = DE, \ BC = EF\end{align*}, and mB>mE\begin{align*}m \angle B > m \angle E\end{align*}, then __________.

## 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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