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