# Angle Bisector Theorem - Midpoints & Line Segments | Summary and Q&A

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August 24, 2017
by
The Organic Chemistry Tutor
Angle Bisector Theorem - Midpoints & Line Segments

## TL;DR

Midpoints divide a segment into two congruent parts, while angle bisectors split an angle into two congruent angles.

## Key Insights

• β Midpoints divide a segment into two congruent parts, allowing for symmetry and equal division.
• πΊ Angle bisectors split an angle into two congruent angles, providing a way to measure and analyze angles.
• π Understanding midpoints and angle bisectors is crucial in solving geometry problems and proving geometric relationships.
• βΊοΈ The value of x can be determined by setting up equations based on congruence relationships between segments or angles.
• π₯³ Ratio relationships between segments can be used to find the lengths of different segments in a figure.
• π Midpoints and angle bisectors have practical applications in real-life scenarios, such as architecture or design.
• πΊ Midpoints are only found on segments, not rays, while angle bisectors always start at the vertex of an angle.

## Transcript

in this lesson we're going to talk about midpoints and angle bisectors so let me give you three pictures and i want you to determine which one is a midpoint is it point a b or c which one is a midpoint a midpoint is a point that divides a segment into two congruent segments point a is not a midpoint because we have a line b is the midpoint because ... Read More

### Q: What is a midpoint?

A midpoint is a point that divides a segment into two congruent segments. It is found on the segment itself.

### Q: How is an angle bisector defined?

An angle bisector is a ray that divides an angle into two congruent angles. It starts at the vertex of the angle and splits it into two equal parts.

### Q: How do you determine if a point is a midpoint?

To determine if a point is a midpoint, compare the lengths of the two segments created by the point. If they are congruent, the point is a midpoint.

### Q: How can angle bisectors be used in problem-solving?

Angle bisectors can be helpful in finding unknown angles or establishing relationships between different angles in a figure.

## Summary & Key Takeaways

• Midpoints are points that divide a segment into two congruent segments.

• Angle bisectors are rays that divide an angle into two congruent angles.

• Midpoints and angle bisectors have various applications in geometry problem-solving.