Geometry-Similar Triangles

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GEOMETRY :

GEOMETRY

:

I can calculate the motion of heavenly bodies, but not the madness of people. 

Crack the codes by answering the given proportions to reveal the person behind this famous quotation:

c n e w t o n A A S I Crack the codes by answering the given proportions to reveal the person behind this famous quotation N I C E 5 = 10 1 = x x = 10 2 = 10 2 x 3 6 4 8 3 x S T O W A 3 = x x = 3 4 = 2 1 = 2 1 = 3 4 16 12 6 6 x 4 x x 27 2 12 9 9 5 4 15 8 6 3 4

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I can calculate the motion of heavenly bodies, but not the madness of people.  Isaac Newton

Congruent Triangles:

Congruent Triangles

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Congruent Triangles

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The same shape but different in size

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Similar Trianges

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Similar Triangles

Similar Triangles :

Similar Triangles have the same shape, but the size may be different . symbol ( ~ )

Instructions::

Instructions: Class will be divided into three groups by color coding Each group will be assign to draw a triangle with specific measurement in inches using a meterstick a. Group1 will make ∆ABC with AB is the longest side b. Group 2 will make ∆DEF with DE is the longest side c. Group 3 will make ∆GHI with GH is the longest side 3. The group will assign their leader to measure each angles. 4. Make a proportion by sharing the work of each group a. Group 1 will take the work of group 2 b. group 2 will take the work of group 3 c. group 3 will take the work of group 1 Then observe the relationship of their sides and angles 5. The group leader and the assistant leader will be the one to present their work.

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D A C B E F G H I ∆ 30 18 24 20 12 16 10 6 8

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D A C B E F G H I AB DE = AC DF = BC EF DE GH = DF GI = EF HI GH AB = GI AC = HI BC ∆ABC ~ ∆DEF ∆DEF ~ ∆GHI ∆GHI ~ ∆ABC 30 18 24 20 12 16 10 6 8

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A B C 90° 35° 90° 35° F E D 90° 35° I H G

Proving Similar Triangles:

Proving Similar Triangles ∆ABC ∆DEF ∆ GHI Measures of Corresponding Sides AB = BC = AC = DE = EF = DF = GH = HI = GI = Measures of Corresponding Angles m ∠ A = m ∠ B = m ∠ C = m ∠ D = M ∠ E = m ∠ F = m ∠ G = m ∠ H = m ∠ I = 30 18 24 20 12 16 10 6 8 35° 35° 35° 55 ° 55 ° 55 ° 90° 90° 90°

COROLLARY: Two triangles similar to a third triangle are similar to each other:

COROLLARY: Two triangles similar to a third triangle are similar to each other ∆ABC ~ ∆DEF ∆DEF ~ ∆GHI ∆GHI ~ ∆ABC

Properties of Similar Triangles:

Properties of Similar Triangles Corresponding angles are congruent (same measure) Corresponding sides are all in the same proportion

35° 60° :

35° 60° 10 35° 60° T U V Y W X 3 5 8 16 6 TV WY UV XY 5 10 5XY 5 = = 3 XY = 30 5 XY 6 =

Checking:

Checking 5 10 3 6 TV WY UV XY 30 = = = 30 ∆TUV ~ ∆WXY

Example 1: Given the following triangles, find the length of s :

Example 1: Given the following triangles, find the length of s A B C D E F = 3

Example 2: Read carefully to see WHAT you are supposed to find.  This problem asks you to find BE. :

Example 2: Read carefully to see WHAT you are supposed to find.  This problem asks you to find BE . Use FULL sides of the triangles, cross multiply and solve. Here are the solutions letting BE = x . 8 x= 36 x = 4.5

Example 3::

Example 3: = 2.7m x

What are the properties of similar triangles?:

What are the properties of similar triangles?

Find x so that each pair of triangles are similar:

Find x so that each pair of triangles are similar 1, 2. 3. 4. 5. x x x

ANSWER::

ANSWER: 1. X = 12 2. X = 20 3. X = 12 4. X = 13.33 5. X = 17.5

ASSIGNMENT::

ASSIGNMENT: Do Testyourself nos. 1-10 on page 152 of your textbook. 2. How to tell the triangles are similar?

Goodbye!!!:

Goodbye!!! Teacher: Mr. Irving S. Ambrona

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