1. Common Core State Standards
Unit 3 Review!
Objective:
to review congruence and similarity
Common Core State Standards
8.G.3; 8.G.4; 8.G.5; 8.G.6; 8.G.7

2. 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.
Congruent Figures: Same size and same shape and congruent corresponding parts. Symbol for congruence is
Always list corresponding vertices in the same order – ORDER IS IMPORTANT!
Tick Marks are used to indicate
congruent segments
Refer to separate facilitator notes for Slides 6 – 23.
Arcs are used to indicate
congruent angles
National Council of Supervisors of Mathematics

3. 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.
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 ~
Always list corresponding vertices in the same order – ORDER IS IMPORTANT!
Refer to separate facilitator notes for Slides 6 – 23.
National Council of Supervisors of Mathematics

4. Use similar figures and proportions:
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.
Refer to separate facilitator notes for Slides 6 – 23.
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
National Council of Supervisors of Mathematics

5. Similar Triangles & Slopes
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)
Refer to separate facilitator notes for Slides 6 – 23.
National Council of Supervisors of Mathematics

6. Area & Perimeter of Similar Figures
Find the ratio of the corresponding side BIG/SMALL (this is the scale factor).
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 9
Refer to separate facilitator notes for Slides 6 – 23.
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
National Council of Supervisors of Mathematics

7. Let’s Practice! Exit Ticket MAP PLUS BOOKLET QUESTIONS
#9, 32, 37, 38, 65, 77, 78
Exit Ticket
After reviewing and practicing Unit 3, rate yourself on how you feel about the same questions in the MAP Plus Book.