Keywords, Theorems and Postulates
Midsegments in Triangles
- Midsegment Theorem
Perpendicular Bisectors and Angle Bisectors in Triangles
- Perpendicular Bisector Theorem
- Perpendicular Bisector Theorem Converse
- Angle Bisector Theorem
- Angle Bisector Theorem Converse
Medians and Altitudes in Triangles
- Median Theorem
Inequalities in Triangles
- Theorem 5-9
- Converse of Theorem 5-9
- Triangle Inequality Theorem
- SAS Inequality Theorem
- SSS Inequality Theorem
Extension: Indirect Proof
If and are the midpoints of the sides they lie on, find:
- The perpendicular bisector of .
- The median of .
- The angle bisector of .
- A midsegment.
- An altitude.
- A triangle has sides with length and . Find the range of the third side.
Fill in the blanks.
- A midsegment connects the __________ of two sides of a triangle.
- The height of a triangle is also called the __________.
- The point of intersection for all the medians of a triangle is the __________.
- The longest side is opposite the __________ angle in a triangle.
- A point on the __________ bisector is __________ to the endpoints.
- A point on the __________ bisector is __________ to the sides.
- A circle is __________ when it touches all the sides of a triangle.
- An __________ proof is also called a proof by contradiction.
- For and , and , 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.