# Intro: GeoGebra skills, terms, vocabulary & postulates

- Author:
- Zawierucha

- Topic:
- Circle, Constructions, Geometry, Terms

## 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 you 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 GeoGebra tools, review some postulates and new vocabulary.

**Part 1 - what you will do on the applet below*****FYI: 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 the figures around. Notice what you can and can't change***

**Directions:**

__A__

__. Two undefined terms: a point and a line__1. 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**

__B. Subsets of a line: the__

**ray**

__and a__

**segment**

__.__vocabulary: ray, segment, midpt. (of a segment)

__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 the midpoint on each of your segments. a. For each of the segments constructed in step 1 & 2: 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: circle, 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**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 name of endpoints 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. Another 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 **circle**** **is all points in the same plane that lie at an equal distance from a center point.
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 other two 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. 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)

## 9. Definition

Define, midpoint

## 10. Definition

Define, congruent (figures)