Topicmf5b27513a4b022c3_1528449000663_0Topic

Applying the properties of similar figures

Levelmf5b27513a4b022c3_1528449084556_0Level

Third

Core curriculummf5b27513a4b022c3_1528449076687_0Core curriculum

VIII.  Planimetry. The student:

9) uses relations between perimeters and areas of similar figures.

Timingmf5b27513a4b022c3_1528449068082_0Timing

45 minutes

General objectivemf5b27513a4b022c3_1528449523725_0General objective

Noticing regularities, similarities and analogies and formulating relevant conclusions.

Specific objectivesmf5b27513a4b022c3_1528449552113_0Specific objectives

1. Calculating lengths of line segments in similar figures.

2. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmf5b27513a4b022c3_1528450430307_0Learning outcomes

The student:

- calculates lengths of line segments in similar figures.

Methodsmf5b27513a4b022c3_1528449534267_0Methods

1. Discussion.

2. Aquarium.

Forms of workmf5b27513a4b022c3_1528449514617_0Forms of work

1. Work in pair.

2. Group work.

Lesson stages

Introductionmf5b27513a4b022c3_1528450127855_0Introduction

The teacher introduces the subject of the lesson - calculating lengths of line segments in similar figuressimilar figuressimilar figures.

Two students chosen by the teacher before prepare materials to have a discussion in the class.

Students revise properties of similar figuresproperties of similar figuresproperties of similar figures and prepare multimedia presentation about similar figures, also showing figures that are not similar.

Proceduremf5b27513a4b022c3_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to identify the scale of similarityscale of similarityscale of similarity of the drawn similar figuressimilar figuressimilar figures.

[Geogebra applet]

Students work with the ‘aquarium’ method. A few participants sit in a circle. Chosen students prepare materials about similar figures they presented at home.

Students in the circle discuss the subject. The rest of the group are observers and sit around them. They analyse the discussion in terms of choosing right arguments and they draw conclusions.

Students’ conclusions:

- Similar figures have the same shape but can have different size.
- Two polygons are similar if the respective angles are equal and respective sides are proportional.
- The scale of similarity is the number expressing the ratio of corresponding line segments in similar figures.mf5b27513a4b022c3_1527752263647_0- Similar figures have the same shape but can have different size.
- Two polygons are similar if the respective angles are equal and respective sides are proportional.
- The scale of similarity is the number expressing the ratio of corresponding line segments in similar figures.

The teacher grades the work of students participating in the discussion and the preparation and way of presenting of the experts. The teacher also pays attention to the focus and analysation of the discussion by the observers.

Students do the exercises in pairs. The first pair that solves the exercises correctly gets a mark.

Task
In what scale the equilateral triangle whose side is $4\sqrt{2}$ is similar to the equilateral triangle whose side $3\sqrt{3}$?

Task 
A rectangle whose dimensions $3\sqrt{2}·5\sqrt{3}$ similar to a rectangle whose shorter side
is equal to $\sqrt{5}$.

Calculate the scale of similarityscale of similarityscale of similarity of the smaller rectangle to the greater rectangle.

Task
Two line segments are similar in the scale 2:5. The longer line segment is 20 cm long. Calculate the sum of the lengths of these line segments.mf5b27513a4b022c3_1527752256679_0Two line segments are similar in the scale 2:5. The longer line segment is 20 cm long. Calculate the sum of the lengths of these line segments.

Task
A triangle ABC whose perimeter is $14\sqrt{2}$ is similar to the triangle A’B’C’ whose sides are 6, 10, 12 long. Calculate the length of the longest side of the ABC triangle.

Task
The square KIndeks dolny 1₁ is similar to the square KIndeks dolny 2₂ in the scale 3. The square KIndeks dolny 3₃ is congruent to the square KIndeks dolny 2₂. Are the squares KIndeks dolny 1₁ and KIndeks dolny 3₃ similar? If yes, give the scale of similarityscale of similarityscale of similarity of these figures.

An extra task:
Draw any three line segments a, b, c. Construct such line segment d that the condition $\frac{a}{b}=\frac{c}{d}$ is met.

Lesson summarymf5b27513a4b022c3_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- Similar figuressimilar figuresSimilar figures have the same shape but can have different size.

- Two polygons are similar if the respective angles are equal and respective sides are proportional.

- The scale of similarityscale of similarityscale of similarity is the number expressing the ratio of corresponding line segments in similar figures.

Selected words and expressions used in the lesson plan

drawing figuresdrawing figuresdrawing figures

properties of similar figuresproperties of similar figuresproperties of similar figures

scale of similarityscale of similarityscale of similarity

similar figuressimilar figuressimilar figures

similarity of figuressimilarity of figuressimilarity of figures