# Angle and Segment Bisectors

- Author:
- Marissa Moore, Terry Lee Lindenmuth

- Topic:
- Constructions

## Section 1

Angles

## Vocabulary

__Ray:__a line that has a point at on end and goes on infinitely in the other direction

__Angle:__Is made up of two rays with two sides that meet at a vertex

__Vertex:__the point were two rays meet to create an angle

__Sides__

**Each ray is that makes up an angle is considered a side**

__:____Right angle:__two rays that meet to form 90 degrees

__Acute angle:__two rays that meet to form less than 90 degrees

__Obtuse angle:__Two rays that meet to form more than 90 degrees

__Contingent angle:__Two angle that have the SAME measure

__Angle Bisector:__A ray, line, or line segment, that divides an angle into two equal parts

## Use the angle tool to find the measure of the angle below.

## 1) Types of angles

What kind of angle is the above angle?

## 2) Types of Angles

Move point A in the angle above to create an obtuse angle

## 3) Interact with this tool on how to construct angle bisectors.

## 4) Use the angle below to create an angle Bisector and then use the angle tool to show they are congruent.

## Naming an angle

To name an angle, 3 points need to be included. One point from either side and the vertex. The vertex is always the middle point.

## 5) Naming an Angle

How do you name the above angle? Select all that apply

## Section 2

Distance and Midpoint

## Vocabulary

__Midpoint:__the point on a segment that is halfway between the segment endpoints

__Segment Bisector:__any segment line or plane that intersects a segment at it's midpoint

__Perpendicular Bisector:__any segment, line, or plane that interests a segment and creates a right angle

__Distance of coordinates:__when finding the distance of coordinates you will find the distance of x and of y

__Distance between two points:__when finding the distance between two points you use the distance formula.

## 6)

Using the distance formula. What is the distance between the two points above? Show your work in the box below using the f(x) button **if it is available** Round your answer to the nearest thousandth (3 decimal places)

## 7) Use the distance tool on the line segment above

Does your answer match?

## If you answer does not match

Explain why and show how to fix your work

## 8) Coordinate Distance

What is the distance between the coordinates? (distance between x values and y values?)

## 9) Interact with this to find how locate the midpoint and create a perpendicular bisector at the midpoint

## 10) Locate the midpoint and draw any bisector. Show that the segments are congruent on either side of the midpoint using the distance tool

## Section 3

Finding bisectors and midpoints quickly using GeoGebra