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 measured
2. precision -smallest unit available on measuring tool
3. precision factor -measurement should be precise to ½ the
smallest unit
4. betweenness of points-relationship stating that points are
collinear and a<n<b.
5. congruent -same measure (shown by a hash mark)
Construction Activity
Step 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.
(a  c  b  6)
Assignment: page 17 #1-10
page 18 #22-24, 28-30, 34-36
page 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 𝑎 − 𝑏
𝑥1+𝑥2 𝑦1+𝑦2
,
)
2
2
midpoint formula
(
distance formula
d=
𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
2
Find the measure by using the number line.
1. AC
2. BE
3. CF
Answer:
Find the measure by using the number line.
1. AC = 3
2. BE = 5
3. CF = 5.5
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 𝑎2 + 𝑏 2 = 𝑐 2
Answer:
Height: 2
Length: 5
a2 + b 2 = c 2
(2)2 + (5)2 = c2
4 + 25 = c2
29 = c2
C = 29
So, the distance is 29.
No graph? No problem! Use the distance formula!
Find the distance between (-3, 2) and (6, 5).
d=
𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
2
Answer
d=
𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
d=
6 − −3
2
+ 5 −2
d = (9)2 + (3)2
d = 81 + 9
d = 90 or 9.49
2
2
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!
𝑥 +𝑥 𝑦 +𝑦
(
Find the midpoint of (8, 4) and (12, 2).
1
2
2
,
1
)
2
2
Answer
(
𝑥1+𝑥2 𝑦1+𝑦2
,
)
2
2
(
8+12 4+2
,
)
2
2
(
20 6
, )
2 2
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 figure
7 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 counterclockwise direction?
The birds were rotated clockwise and the fish
counterclockwise.
ASSIGNMENT:
TRANSFORMATION WORKSHEET, DUE NEXT CLASS PERIOD