GEOMETRY OUTCOME 1

CHAPTER 1 AND 3, WITH ADDED COMPONENTS

CHAPTER 1, SECTION 1 VOCABULARY

1. point-location on a plane, shown by a dot

2. Line- straight connection of at least 2 points

3. Plane-flat surface

4. Collinear-points on the same line

5. Coplanar-points on the same plane

6. Coordinate plane-typical graph having an x and y axis

7. Origin-point (0,0) on a coordinate plane

EXAMPLES OF REAL LIFE POINTS, LINES, AND PLANES

• Points: needle point, pencil lead tip, dot of any punctuation mark• Lines: stripes, corners of rooms, grass edge• Planes: textbook cover, football field, table top

Can you name more?

NAMING POINTS, LINES, AND PLANES

How would you name point V?

How would you name the line going through points S, P, and T?

How would you name the quadrilateral plane?

GRAPHING POINTS ON A COORDINATE PLANE

• Start at the origin, always• Go left (negative) or right (positive)

the first number• Then go up (positive) or down

(negative) the second number• Draw your dot• Label!!!

PREPPING FOR SECTION 2

• Remember these from middle school? Yeah…they don’t go away.

< less than> Greater than= Equal

CHAPTER 1, SECTION 1 ASSIGNMENT

Handout 1.1 has a coordinate plane on the front for you to graph and label 10 points.

Then work page 9 #1-18 and page 11 #51-56 on the same paper.

When you are finished: review it, make sure your name is on it, and turn it in. It is due next class period at the beginning of the block.

OUTCOME 1, CHAPTER 1, SECTION 2

LINEAR MEASURE AND PRECISION

Chapter 1, Section 2 Vocabulary

1. line segment -line with 2 endpoints, can be measured2. precision -smallest unit available on measuring tool3. precision factor -measurement should be precise to ½ the smallest unit4. betweenness of points-relationship stating that points are collinear and a<n<b.5. congruent -same measure (shown by a hash mark)

Construction ActivityStep 1: Construct a rectangle that is 3 inches by 1 inch.

Step 2: Find the precision factor for the rectangle and write it inside.

Step 3: Draw a parallelogram plane measuring 5 inches by 3 inches and label as m.

Step 4: Construct a line going through the parallelogram containing points B, R, and P.

Step 5: Construct a line segment contained within plane m, intersecting line BR at point P, and measuring 2 inches.

Step 6: Draw a line segment AC that measures 6 inches.

Step 7: If AB is twice as long as BC, and point B lies between A and C, label the length of AB and BC above the line segment.

Step 8: Use your ruler to measure the following: textbook, desk width, colored paper, and writing utensil. Write these measurements with labels on the back of your colored paper.

Preparing for next class:If a = 5, b = 2, and c = 3, solve the following:

1. ab – c 2. ac + b2 3. )6( bca

Assignment: page 17 #1-10page 18 #22-24, 28-30,

34-36page 20 #62-72

Due at the beginning of class next time.

Outcome 1, Chapter 1, Section 3

Midpoint and Distance Formulas

Chapter 1, Section 3 Vocabulary Terms

midpoint-point in the middle of a segment, creating 2 congruent segments

segment bisector – any segment, line, or plane that intersects a segment at its midpoint

distance – measure between two points, ALWAYS positive, can be found by counting on a number line, Pythagorean theorem, or

midpoint formula ( , )

distance formula d =

Find the measure by using the number line.

1. AC

2. BE

3. CF

Find the measure by using the number line.

1. AC = 3

2. BE = 5

3. CF = 5.5

Answer:

What if the line isn’t horizontal or vertical? How do you find the distance between points? PYTHAGOREAN THEOREM!

* Draw a right triangle and use + =

Answer:

Height: 2

Length: 5

a2 + b2 = c2

(2)2 + (5)2 = c2

4 + 25 = c2

29 = c2

C =

So, the distance is .

No graph? No problem! Use the distance formula!

Find the distance between (-3, 2) and (6, 5).

d =

Answer

d =

d =

d =

d =

d = or 9.49

Find the midpoint of segment CD.

Count using the number line and find the exact middle.

Answer

The midpoint is – .5 or -1/2.

No number line and given an ordered pair? Use the midpoint formula! Simply add the x’s and divide by 2, then add the y’s and divide by 2!

Find the midpoint of (8, 4) and (12, 2).

( , )

Answer

( , )

( , )

( , )

The midpoint is (10, 3).

Find the missing endpoint given that B is the midpoint of AC and A (2, 3), B (4, 7).

WILL WORK THIS ONE ON THE BOARD ---

Assignment:worksheet 1.3 #1 – 17

*Due next class period.

Topic: Shapes and Transformations Wednesday, 9.4.13

*Reminder: Review on Friday and Outcome TEST on Tuesday, September 10th!

Geometry, Outcome 1, Component 1-3 wrap up

Types of Polygons, Named by Number of Sides

Name Sides Angles

Triangle 3 3

Quadrilateral 4 4

Pentagon 5 5

Hexagon 6 6

Heptagon 7 7

Octagon 8 8

Nonagon 9 9

Decagon 10 10

To transform something is to change it. In geometry, there are specific ways to describe how a figure is changed. The transformations you will learn about include:

• Translation

• Rotation

• Reflection

• Dilation

Renaming Transformations

It is common practice to name shapes using

capital letters:

It is common practice to name transformed

shapes using the same letters with a “prime” symbol:

A translation "slides" an object a fixed distance in a given direction.  The

original object and its translation have the same shape and size, and they

face in the same direction.

Translations are SLIDES!

Let's examine some

translations related to coordinate geometry.

 

The example shows how each vertex moves the same distance in

the same direction.

Write the Points

• What are the coordinates for A, B, C?

• What are the coordinates for A’, B’. C’?

• How are they alike?• How are they different?

In this example, the "slide"  moves

the figure7 units to the

left and 3 units down. (or 3

units down and 7 units to the

left.)

Write the points

• What are the coordinates for A, B, C?

• What are the coordinates for A’, B’, C’?

• How did the transformation change the points?

A rotation is a transformation that turns a figure about a fixed point called the center of rotation.  An object and its rotation are the same shape and size,

but the figures may be turned in different directions.

The concept of rotations can be

seen in wallpaper

designs, fabrics, and art work.

            Rotations are TURNS!!!

                                           

 

This rotation is 90 degrees

counterclockwise.

Clockwise

         

Counterclockwise

         

A reflection can be seen in water, in a mirror, in glass, or in a shiny surface.  An object and its

reflection have the same shape and size, but the figures face in opposite directions.  In a mirror,

for example, right and left are switched.

            

 

Line reflections are FLIPS!!!

              

               

   

                  

         

The line (where a mirror may be placed) is called the line of reflection.  The distance from a point to the line of reflection is the

same as the distance from the point's image to the line of reflection.

A reflection can be thought of as a "flipping" of an object over the line of reflection.

If you folded the two shapes together line of reflection the two shapes would overlap

exactly!

What happens to points in a Reflection?

• Name the points of the original triangle.

• Name the points of the reflected triangle.

• What is the line of reflection?

• How did the points change from the original to the reflection?

A dilation is a transformation that produces an image that is the same shape as the original,

but is a different size.

A dilation used to create an image larger than the original is called an enlargement.  A

dilation used to create an image smaller than the original is called a reduction.

Dilations always involve a change in size.

                                              

Notice how EVERY

coordinate of the original triangle has

been multiplied by

the scale factor (x2).

REVIEW: Answer each question………………………..

Does this picture show a translation,

rotation, dilation, or reflection?

How do you know?

Rotation

Does this picture show a

translation, rotation, dilation,

or reflection?

How do you know?

Dilation

Does this picture show a translation, rotation, dilation, or

reflection?

How do you know?

(Line) Reflection

Which of the following lettered figures are translations of the

shape of the purple arrow?  Name ALL that apply.

Explain your thinking.

Letters a, c, and e are translations of the purple

arrow.

Has each picture been rotated in a clockwise or counter-clockwise

direction?

The birds were rotated clockwise and the fish

counterclockwise.

ASSIGNMENT:TRANSFORMATION WORKSHEET, DUE NEXT CLASS PERIOD