6 4 and 6 5 congruent and similar triangles
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6.4 and 6.5 Congruent and Similar Triangles PowerPoint PPT Presentation


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6.4 and 6.5 Congruent and Similar Triangles. Similar and Congruent Figures. Congruent polygons have all sides congruent and all angles congruent. Similar polygons have the same shape; they may or may not have the same size. Tests for Congruency. Ways to prove triangles congruent :

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6.4 and 6.5 Congruent and Similar Triangles

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6 4 and 6 5 congruent and similar triangles

6.4 and 6.5Congruent and Similar Triangles


Similar and congruent figures

Similar and Congruent Figures

  • Congruent polygons have all sides congruent and all angles congruent.

  • Similar polygons have the same shape; they may or may not have the same size.


Tests for congruency

Tests for Congruency

Ways to prove triangles congruent :

  • SSS ( Side – Side – Side )

  • SAS ( Side – Angle – Side )

  • ASA ( Angle – Side – Angle ) or AAS ( Angle –Angle – Side )

  • RHS ( Right angle – Hypotenuse – Side )


Thinking time

Thinking Time ?????

  • If 3 angles on A are equal to the 3 corresponding angles on the other B, are the two triangles congruent ?


Similar triangles

?

2cm

4 cm

65o

25o

?

12cm

Similar triangles

For two similar triangles,

  • Similar triangles are triangles with the same shape

  • corresponding angles have the same measure

  • length of corresponding sides have the same ratio

Example

Side = 6 cm

Angle = 90o


Similar triangles1

Similar Triangles

3 Ways to Prove Triangles Similar


6 4 and 6 5 congruent and similar triangles

Similar triangles are like similar polygons. Their corresponding angles are CONGRUENT and their corresponding sides are PROPORTIONAL.

10

5

6

3

8

4


But you don t need all that information to be able to tell that two triangles are similar

But you don’t need ALL that information to be able to tell that two triangles are similar….


Aa similarity

AA Similarity

  • If two angles of a triangle are congruent to the two corresponding angles of another triangle, then the triangles are similar.

25 degrees

25 degrees


Sss similarity

SSS Similarity

  • If all three sides of a triangle are proportional to the corresponding sides of another triangle, then the two triangles are similar.

21

14

18

8

12

12


Sss similarity theorem

SSS Similarity Theorem

If the sides of two triangles are in proportion, then the triangles are similar.

D

A

C

B

F

E


Sas similarity

SAS Similarity

  • If two sides of a triangle are proportional to two corresponding sides of another triangle AND the angles between those sides are congruent, then the triangles are similar.

14

21

18

12


Sas similarity theorem

SAS Similarity Theorem

D

A

C

B

F

E

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.


6 4 and 6 5 congruent and similar triangles

D

A

C

B

F

E

SAS Similarity Theorem

Idea for proof


Name similar triangles and justify your answer

Name Similar Triangles and Justify Your Answer!


6 4 and 6 5 congruent and similar triangles

A

80

D

E

80

B

C

ABC ~ ADE by AA ~ Postulate


6 4 and 6 5 congruent and similar triangles

C

6

10

D

E

5

3

A

B

CDE~ CAB by SAS ~ Theorem


6 4 and 6 5 congruent and similar triangles

L

5

3

M

6

6

K

N

6

10

O

KLM~ KON by SSS ~ Theorem


6 4 and 6 5 congruent and similar triangles

A

20

D

30

24

16

B

C

36

ACB~ DCA by SSS ~ Theorem


6 4 and 6 5 congruent and similar triangles

L

15

P

A

25

9

N

LNP~ ANL by SAS ~ Theorem


Home work

Home Work 


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