Angle and Segment Bisectors

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?

Check all that apply

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

Check 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?

Check all that apply

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

11) Use the tools available to create an angle bisector, find the midpoint and create a perpendicular bisector. Show that the angles and the line segments are congruent using the distance tools