Intro 2: GeoGebra skills, terms, vocabulary & postulates
About this activity
The objectives of this activity:
With the GeoGebra app:
1. you will become familiar with some of the tools used in GeoGebra.
2. you will explore what you can and can't change once you have constructed a figure.
3. You will work with 2 of the three undefined terms, point & line, in order to illustrate some postulates.
With the follow-up questions:
1. You will review and extend your understanding of the postulates and definitions you encountered
2. You will review the vocabulary used in this activity.
3. You will use the Applet to make some observations and write some conclusions.
What you should do in your notebook:
1. Add any new vocabulary to your vocabulary section.
2. Write down questions and correct answers for any questions that you weren't sure about and/or got incorrect.
3. Keep track of new observations and facts that helps you extend your understanding of the material covered.
Tools reference sheet to be used with GeoGebra Activities - the tools we will use in this activity are highlighted. ****use Ctrl + Shift + Click to open a link in a new tab ***
Getting comfortable with some tools of GeoGebra, some postulates and vocabulary.
Part A - what you will do on the applet below
Directions:
***once you have drawn something always go back to the move tool (or hit esc on keyboard) in order interact with what you have on the screen. Move your figures around. Notice what you can and can't change***
A. Construct a diameter
1. Construct a circle using the Circle with Center through point tool.
2. Use the line tool to construct a line that contains the circle's center and the point on the circle.
3. This line contains the diameter & 2 radii ( 1 diameter = 2 radii)
B. Use Show/hide tool to illustrate the diameter
1. Select Show/hide tool and then the line you constructed, then select the segment tool.
2. You should have 2 pts on the circle, they are the endpoints of a diameter. With the segment tool still selected; select those two points to construct a diameter.
Use the point tool and plot two points, then use the line tool to construct a line.
What you have just done is illustrated the following postulate: "Through 2 points there is exactly one line"
Definition, postulate -A geometric statement whose truth is assumed without a proof.
Clear your screen
C. Explore - use any tools you want to
1. Construct a circle again.
2. See if it is possible to construct a diameter another way.
there
1. Use the ray tool to draw a ray, the first point that is illustrated is its endpoint.
2. Use the segment tool to draw a segment.
3. Use Segment with Given length tool to draw another segment.
4. Use the midpoint tool to locate a midpoint on your two segments.
a. use the distance/length tool to measure the length of the two segments formed by the midpoint.
b. Construct a line. Can you get a midpoint for your line?
Clear your screen
C. Circles constructed two ways. Vocabulary: center, point on a circle, radius.
1. Construct your first circle using the Circle with Center through point* tool - *that point is on the circle.
2. Construct your 2nd circle using the Circle: Center* & radius tool - *the center is point in the interior of the circle.
Use the move tool to explore what you can and can't change about the 2 circles.
3. First, delete your 2nd circle. Construct a radius for your 1st circle using the segment tool.
4. Construct a 2nd radius for that circle but this time use Segment with Given length tool And instead of writing in a specific value enter the endpoints' name of the first radius for example AB - the capital letters side by side is the symbol that stands for: "the length of segment AB".
Do this once more. You will now have 3 radii (plural for radius) for your circle.
5. Use the distance or length tool to get the length of all three radii.
Clear your screen
D. One more postulate.
1. use the line tool to construct 2 lines that intersect.
2. Use the intersect tool to get their point of intersection.
You have illustrated the postulate: "if two lines intersect, then they intersect in exactly one point."
Some of the questions will talk about congruence. Watch this short video before you answer the questions.
1. Short answer
We encountered 2 postulates in this activity: 1. Through 2 points there is exactly one line 2. if two lines intersect, then they intersect in exactly one point. In your own words describe what each postulate is saying.
2. Definition
A radius of a circle is a segment whose endpts are the center of the circle and a point on the circle. A diameter is a chord that contains the center of the circle. Define, chord (of a circle)
3. Definition
Define, ray.
4. Short answer
In plane geometry we have three undefined terms one is "plane" ( a 2-dimensional surface that extends out indefinitely into space), what are the two other undefined terms mentioned in this activity.
5. Definition
Define, postulate.
6. Definition
Define, segment.
7. Explain
Explain why the following statement must be true: in a circle or in congruent circles, radii or diameters are congruent. (make sure to watch the video that explains congruent figures)
8. Define
Define, midpoint.
9. Fill-in
a. A circle has ________ radii and diameters. b. A segment has ________ midpoint(s). c. A line has ______ midpoint(s). possible answer choices: zero, one, two, three, infinite (unlimited)
10. Definition
Define, midpoint
11. Definition
Define, congruent (figures)