Geometry Chapter 6: Properties of Triangles and Midsegments

Overview

• Discusses properties of triangles and midsegments used to solve triangle problems.
• Defines key concepts: perpendicular bisectors, angle bisectors, medians, altitudes, and midsegments.
• Includes theorems about equidistance from bisectors and midsegment properties.
• Provides examples to find missing side lengths and angles in triangles.
• Learning target: Using special triangle properties and midsegments to solve problems.

Key Concepts

Perpendicular Bisectors

• Theorem 6.1: In a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
• The converse of Theorem 6.1 is also true.

Angle Bisectors

• Theorem 6.3: If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.
• The converse of Theorem 6.3 is true.

Midsegments

• A midsegment in a triangle is parallel to the opposite side and half its length.

Theorems

• Perpendicular Bisector Theorem: A point on the perpendicular bisector is equidistant from the segment's endpoints.
• Angle Bisector Theorem: A point on the angle bisector is equidistant from the sides of the angle.

Examples

• Example 1: Instructions to find the measure of segments RS and AD using triangle properties.

Learning Target

• Utilize properties of triangles and midsegments effectively to solve various triangle-related problems.

Sections Covered

• 6.1 & 6.4: Focus on properties of triangles and midsegments.

Applications

• Using these properties and theorems can help solve problems involving missing side lengths and angles in triangles.

Diagrams and Visuals

• Various visuals included to help illustrate concepts such as the Perpendicular Bisector Theorem and Angle Bisector Theorem.

This summary captures the essential concepts and theorems presented in Geometry Chapter 6, providing a basis for further study or review.