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

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

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

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

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

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

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.