1. 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

2. Let’s Explore!! I-ready Textbook- Period 1 Work with your partner: Complete pg 162-164 Independently: Will be collected Complete 165

3. Transformations The four main Transformations are: Translation (Slide)Reflection (Flip) Rotation (Turn)Dilation (Scale)

4. 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)

5. Rotation Rules: 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.

6. 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 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.

7. 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

8. Let’s Practice I-ready Textbook Period- 2 Independently 1.Complete pg 168 - 173 Assessment – Will be collected 2.Answer pg 174 - 175

9. 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 9 Always list corresponding vertices in the same order – ORDER IS IMPORTANT! Tick Marks are used to indicate congruent segments Arcs are used to indicate congruent angles

10. 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 ~ 10 Always list corresponding vertices in the same order – ORDER IS IMPORTANT!

11. Angle-Angle Similarity If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. 11 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

12. 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 Types of Slopes Positive NegativeZero Undefined

13. Area & Perimeter of Similar Figures 39 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. 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*3 2 = 9*9 = 81

14. Let’s Practice I-ready Textbook Period- 3 Independently 1.Complete pg 178- 181 Assessment – Will be collected 2.Answer pg 182 - 183

15. Period 3- Types of Angles Matching! Transversal A line that cuts across two or more (usually parallel) lines Exterior angles that are on opposite sides of the transversal (equal to each other) Interior angles that are on opposite sides of the transversal (equal to each other) Alt Ext. Angles Alt Int. Angles Corr. Angles Angles in the same position with respect to the lines and transversal (equal to each other) Vertical Angles Angles that are opposite from each other formed by the intersection of 2 lines (equal to each other)

17. All About Triangles! x° y° z° The sum of the measures of the interior angles of a triangle is 180 ° x° + y° + z° = 180° The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. x° y° p° x° + y° = 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 2 + b 2 = c 2 a b c

18. Midpoint & Distance on the Coordinate Plane Midpoint Distance

19. 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

20. Let’s Practice I-ready Textbook Period- 4 Independently 1.Complete pg 192 -194 Assessment – Will be collected 2.Answer pg 195

21. Let’s Practice I-ready Textbook Period- 5 Independently 1.Complete pg 215 - 217 Assessment – Will be collected 2.Answer pg 218 - 219

22. 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

23. 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

24. Let’s Practice I-ready Textbook Period- 7 Independently 1.Complete pg 229 - 233 Assessment – Will be collected 2.Answer pg 234- 235

25. Unit 3 – Interim Assessment I-ready Textbook Period 9 Complete pg 236 - 238

26. 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.