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Unit 2 Review!
Objective:
to review the concept of congruence
Common Core State Standards:
8.G.1; 8.G.2; 8.G.5; 8.G.6; 8.G.7
Let’s Explore!!
I-ready Textbook- Period 1
Work with your partner:
Complete pg 162-164
Independently: Will be collected
Complete 165
Transformations
The four main Transformations are:
Translation (Slide)
Reflection (Flip)
Rotation (Turn)
Dilation (Scale)
A translation is a transformation that slides a
figure in any direction.
Translation Rule:
Ta,b (x, y) = (x + a, y + b)
Example
T0,4 (2, 3) = (2 + 0, 3 + 4) = (2, 7)
A rotation is a transformation that turns a figure
about a fixed point called the center of rotation.
The measure of the rotation is the angle of
rotation.
Rotation Rules:
A reflection is a transformation that flips a figure
over a 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.
Reflection Rules:
Y axis: (x, y)  (-x, y)
X-Axis: (x, y)  (x, -y)
Y=X: (x, y)  (y, x)
Y=-X: (x, y)  (-y, -x)
A dilation is a transformation that makes a figure
larger or smaller. This means the two figures are
similar (same shape/different size).
A scale factor is the ratio of the side lengths of
the image to the corresponding side lengths of the
original figure.
Dilation Rule:
(x,y)  (kx, ky)
k>1: enlargement
0<k<1: reduction
Let’s Practice
I-ready Textbook
Period- 2
Independently
1. Complete pg 168 - 173
Assessment – Will be collected
2. Answer pg 174 - 175
Congruence
A two-dimensional figure is congruent to another if the second can
be obtained from the first by a sequence of rotations, reflections,
and translations. Always list corresponding vertices in the same order –
ORDER IS IMPORTANT!
Congruent Figures: Same size and same shape and congruent
corresponding parts. Symbol for congruence is
Tick Marks are used to indicate
congruent segments
Arcs are used to indicate
congruent angles
9
Similarity
A two-dimensional figure is similar to another if the second can be
obtained from the first by a sequence of dilations, rotations,
reflections, and translations.
Always list corresponding vertices in the same order –
ORDER IS IMPORTANT!
Similar Figures: Same shape but size may be different (due to a
dilation). Corresponding angles are congruent and corresponding
sides are proportional (constant ratio between all sides-BIG/SMALL
or SMALL/BIG). Symbol for similarity is
10
~
Angle-Angle Similarity
If two angles of one triangle are congruent to two angles of another
triangle, then the triangles are similar.
Indirect Measurement
Indirect Measurement is a technique that uses proportions to find a
measurement when it is not possible to measure something directly.
Use similar figures and proportions:
1) Draw a sketch to identify similarities (height/width/shadow etc.)
2) Create a proportion substituting values for the given measurements
3) Solve for X
11
Types of Slopes
Positive
Negative
Zero
Undefined
Similar Triangles & Slopes
The ratio of the rise to the run of two slopes triangles formed by a line is
equal to the slope of the line (HEIGHT OVER WIDTH)
12
Area & Perimeter of Similar Figures
1) Find the ratio of the corresponding side BIG/SMALL (this is the scale
factor).
2) The perimeter of the bigger figure is equal to the perimeter of the
smaller figure times the scale factor.
3) The area of the bigger figure is equal to the area of the smaller figure
times the scale factor squared.
3
1) Scale Factor = 9/3 = 3
2) Perimeter of small figure = 12. Perimeter of big figure is 12*3 = 36
3) Area of small figure = 9. Area of big figure is 9*32 = 9*9 = 81
9
Let’s Practice
I-ready Textbook
Period- 3
Independently
1. Complete pg 178- 181
Assessment – Will be collected
2. Answer pg 182 - 183
Period 3- Types of Angles Matching!
Transversal
Exterior angles that are on opposite sides of
the transversal (equal to each other)
Alt Int. Angles
Angles in the same position with respect
to the lines and transversal (equal to each
other)
Alt Ext. Angles
Angles that are opposite from each other
formed by the intersection of 2 lines
(equal to each other)
Corr. Angles
Vertical Angles
A line that cuts across two or more
(usually parallel) lines
Interior angles that are on opposite sides
of the transversal (equal to each other)
All About Triangles!
The sum of the measures of the interior angles of a triangle is 180°
y°
x° + y° + z° = 180°
x°
z°
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two
remote interior angles.
y°
x°
x° + y° = p°
p°
Pythagorean Theorem: In a right triangle, the square of the lengths of the hypotenuse c is
equal to the sum of the squares of the lengths of the legs a and b.
a
c
a2 + b2 = c2
b
Midpoint & Distance
on the Coordinate Plane
Midpoint
 x1  x2 y1  y2 
M
,

2 
 2
Distance
d  ( x2  x1 )  ( y2  y1 ) .
2
2
Let’s Explore
I-ready Textbook
Period- 3
Work with your partner:
1. Complete pg 186 - 1888
Assessment – Will be collected
2. Answer pg 189
Let’s Practice
I-ready Textbook
Period- 4
Independently
1. Complete pg 192 -194
Assessment – Will be collected
2. Answer pg 195
Let’s Practice
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Period- 5
Independently
1. Complete pg 215 - 217
Assessment – Will be collected
2. Answer pg 218 - 219
Volume of Cylinders, Cones & Spheres
The volume of a 3D figure is the amount of space that the object
occupies. The volume is the number of cubes the object can hold. Each
cube represents a unit of measure called a cubic unit
V = (p r )(h)
2
1
2
V = ( )(p r )(h)
3
4
3
V = ( )(p r )
3
Let’s Practice
I-ready Textbook
Period- 6
Work With your partner
1. Complete pg 222-224
Assessment – Will be collected
2. Answer pg 225
Let’s Practice
I-ready Textbook
Period- 7
Independently
1. Complete pg 229 - 233
Assessment – Will be collected
2. Answer pg 234- 235
Unit 3 – Interim Assessment
I-ready Textbook
Period 9
Complete pg 236 - 238
Let’s Practice!
MAP PLUS BOOKLET
QUESTIONS
#8, 18, 34, 36, 43, 44, 56, 64
Exit Ticket
After reviewing and practicing Unit 2, rate
yourself on how you feel about the same
questions in the MAP Plus Book.