1. Similarity and Congruence Identifying Similarity and Congruence Finding Missing Measures POLYGONS Irma Crespo 2010

2. Warm Up Which are similar? Which are congruent? SIMILAR same shape; different size CONGRUENT same shape; same size

3. Congruence Congruent polygons have the same measures: same lengths and same angles. congruent triangles 93° 38° 49° 5.4 cm

4. Congruence Matching parts are corresponding parts. In congruent polygons, corresponding parts are equal. l k j i o p n m

5. AB JM = AC JK Similarity Similar polygons have corresponding angles with the same measure AND the ratio of their corresponding sides are proportional. AB 6 DC 6 14 Corresponding angles are equal: each pair has 90° L J 1.5 M 3.5 K 1.5 Corresponding sides are proportional. CD KL = BD LM 6 1.5 = 14 3.5 4

6. Similar Polygons? (OHP) Are corresponding angles equal? Are corresponding sides proportional?

7. Find Missing Measures Given that rectangle LMNO is similar to rectangle GHIJ, find the missing measure. J G 2 I H 4 3 LM ON m LO GI = NO JI = 3232 rectangle LMNO rectangle GHIJ m4m4 2m = 3(4) 2m = 12 m = 6

8. Finding Measures (OHP)

9. Summary To determine if polygons are similar find out if the corresponding angles are similar and the corresponding sides are proportional. To find missing measures on similar polygons, perform cross multiplication and solve for the variable.

10. Exit Slip Find the missing measure for the similar polygons. 24 x 3 6 48 12

11. Practice Worksheet Complete the practice worksheet. Work with a partner or on your own. Submit completed worksheet for grading. Solutions are discussed the next day.

12. Main Resources http://www.absorblearning.com/mathematics/demo/u nits http://www.absorblearning.com/mathematics/demo/u nits Math Connects: Concepts, Skills, and Problem Solving; Teacher Edition; Course 3, Volume 1 Columbus:McGraw-Hill, 2009. PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of Education. Winter 2010. Lesson plan and presentation were created under the supervision of Mrs. Papanastasopoulos of O.W. Best Middle School in Dearborn Heights, Michigan.