Congruence and similarity of triangles

Similarity and CongruenceObjectivesStudents will know how to determine that two figures are similar or congruent byinvestigating figures that are similar and figures that are congruent. Then they willknow how to prove that two figures are similar or congruent by using definitions,postulates, and theorems.Core Learning Goals2.1.1The student will analyze the properties of geometric figures.2.2.1The student will identify and/or verify congruent and similar figures and/orapply equality or proportionality of their corresponding parts.Materials NeededWorksheets, calculator, paper, ruler, formula sheet, protractor, patty paperPre-requisite Concepts NeededStudents will need to be able to measure segments using a ruler, measure angles usinga protractor, and be familiar with the theorems and postulates used to prove figuressimilar and congruent.Approximate TimeOne 30 minute lesson for the discovery lesson and up to 60 minutes for the practice,depending on how well students remember the above-mentioned pre-requisite skills.HSA Geometry ActivitiesActivity 6Page 138Page 1
Similarity and CongruenceLesson PlanWarm-Up/Opening ActivityUse the Prediction Guide to determine what students already know. Feel free toadd/delete/change statements as they fit your class.Accept students’ answers and justifications and ask if the class thinks they arereasonable.Answers:1.Disagree2.Disagree3.Agree4.Agree5.AgreeDevelopment of IdeasWorksheet: Comparing Sizes of FiguresAsk students to work in groups of 2 or 3 to measure all of the segments listed using aruler. It is helpful if all students measure using the same unit (suggest measuring incentimeters). It may be helpful to have the students change their ratios to a decimal(about 1.4) to show that the ratios are equal.Answers:The ratio is about 9:6.5 [due to differences in printing and copying,you will need to check these measurements carefully]1.12 cm:8.6 cm (about 1.4)2.8.8 cm:6.1 cm (about 1.4)3.6.5 cm:4.5 cm (about 1.4)4.41.6 cm:29.4 cm (about 1.4)2.90 ̊ and 90 ̊6.85 ̊ and 85 ̊7.102 ̊ and 102 ̊8.105.6 cm²:52.46 cm² (about 2)9.The ratio of the lengths stays the same in an enlargement, theangle measures stay the same, the perimeters are in the sameratio as the enlargement, and the areas increase by (ratio)².10.The segment length in photo 1 should be about 7 cm.11.The angle measure in photo 1 would be 20º.HSA Geometry ActivitiesActivity 6Page 139Page 2