2. Warm-Up SILENTLY… 1.Get out a blank sheet of paper, and a pencil. 2.Wait quietly for further instructions.

3. Thinking Maps are visual tools for learning, and include eight visual patterns each linked to a specific cognitive process. Each diagram type is intended to correspond with eight different fundamental thinking processes. They are supposed to provide a common visual language to information structure, often employed when students take notes. Circle Map used for defining in context Bubble Map used for describing with adjectives Flow Map used for sequencing and ordering events Brace Map used for identifying part/whole relationships Tree Map used for classifying or grouping Double Bubble Map used for comparing and contrasting Multi-flow map used for analyzing causes and effects Bridge map used for illustrating analogies

5. CIRCLE MAP CIRCLE MAP Thinking Skill: Defining in Context & Brainstorming Main Idea or Concept Ideas, examples, definition How do you know this?

6. On your paper, create your circle map. Unit 1

7. Unit 1: Transformations, Congruence, and Similarity Standards: MCC8.G.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. MCC8.G.2 Understand that 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; given two congruent figures, describe a sequence that exhibits the congruence between them. MCC8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two ‐ dimensional figures using coordinates. MCC8.G.4 Understand that a two ‐ dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two ‐ dimensional figures, describe a sequence that exhibits the similarity between them. MCC8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle ‐ angle criterion for similarity of triangles.

8. Math 8 Day 4 Learning Target: Students can set up proportions for similar figures and solve for the missing side.

9. Similar Figures Goal 1 Identify Similar Polygons Goal 2 Find the missing value Goal 3Describe a sequence that exhibits the similarity between two similar two‐dimensional figures

10. Similar polygons are polygons for which all corresponding angles are congruent and all corresponding sides are proportional. Example:

11. Similar Polygons Polygons are said to be similar if : a)there exists a one to one correspondence between their sides and angles. b) the corresponding angles are congruent and c) their corresponding sides are proportional in lengths.

12. Definition of Similar Polygons - Two polygons are SIMILAR if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.

13. In the diagram, pentagon GHIJK is similar to (~) pentagon ABCDE, if all corresponding sides are proportional GHIJK ~ ABCDE

14. Find the value of x, y, and the measure of  P if  TSV ~  QPR. x = 6 y = 10.5  P = 86° Example 1

15. Example 2 Trapezoid ABCD is similar to trapezoid PQRS. List all the pairs of congruent angles, and write the ratios of the corresponding sides in a statement of proportionality.  A   P,  B   Q,  C   R,  D   P

16. Example 3 Decide if the triangles are similar. The triangles are not similar.

17. Example 4 You have a picture that is 4 inches wide by 6 inches long. You want to reduce it in size to fit a frame that is 1.5 inches wide. How long will the reduced photo be?

18. Sequences That Exhibit Similarity You can use sequences of translations, reflections, rotations, and dilations to determine if 2 figures are similar. Meaning, look at the 2 figures. If you were to slide, flip, rotate, enlarge, or shrink the first figure, would it then be congruent to the second figure?

19. / A  / E; / B  / F ; / C  / G ; / D  / H AB/EF = BC/FG= CD/GH = AD/EH The scale factor of polygon ABCD to polygon EFGH is 10/20 or 1/2 Scale factor: The ratio of the lengths of two corresponding sides of similar polygons

20. In figure, there are two similar triangles.  LMN and  PQR. This ratio is called the scale factor. Perimeter of  LMN = 8 + 7 + 10 = 25 Perimeter of  PQR = 6 + 5.25 + 7.5 = 18.75

21. Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding sides. If ABCD ~ SPQR, then

22. Find the Missing Value To find the missing value, set up a proportion, cross multiply, then divide to find the missing value.

23. Example 5 Parallelogram GIHF is similar to parallelogram LKJF. Find the value of y. Y = 19.2

24. Example 6: The triangles CAT and DOG are similar. The larger triangle is an enlargement of the smaller triangle. How long is side GO? C A TG O D 1.5 cm 3 cm 2 cm 3 cm 6 cm ? cm Each side and its enlargement form a pair of sides called corresponding sides. (1) Corresponding side of TC --> GD (2) Corresponding side of CA--> DO (3) Corresponding side of TA--> GO Length of corresponding sides GD=3 TC=1.5 DO=6 CA=3 GO=? TA=2 Ratio of Lengths 3/1.5=26/3=2?/2=2 The scale factor is 2.

25. 1.5 cm 2 cm 3 cm T C (1) Each side in the larger triangle is twice the size of the corresponding side in the smaller triangle. A G D O 3 cm 6 cm ? cm (2) Now, let’s find the length of side GO i) What side is corresponding side of GO? TA ii) What is the scale factor? 2 iii) Therefore, GO= scale factor x TA iv) So, GO= 2 x 2 = 4 cm

26. What did we just learn about similar polygons ? Same shape Different size Corresponding sideSize-change factor Equal angles Similar polygons

27. Example 1: Quadrangles ABCD and EFGH are similar. How long is side AD? How long is side GH? (1)What is the scale factor? (2)What is the corresponding side of AD ? (3)How long is side AD? (4)What is the corresponding side of GH? (5)How long is side GH? 12÷ 4= 3 & 18÷ 6=3 EH AD = 5 CD 7 x 3 = GH, GH = 21

28. Example 2 : Figure MORE is similar to Figure SALT. Select the right answer with the one of the given values below. (1) The length of segment TL is a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cmabcd (2) ER corresponds to this segment. a. TS b. TL c. AL d. SAabcd (3) EM corresponds to this segment. a. TS b. TL c. SA d. ALabcd (4) The length of segment MO. a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cmabcd M O RE T S A L