6 4 and 6 5 congruent and similar triangles
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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
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


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

10

5

6

3

8

4



Aa similarity
AA Similarity that two triangles are similar….

  • 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 that two triangles are similar….

  • 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 that two triangles are similar….

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

D

A

C

B

F

E


Sas similarity
SAS Similarity that two triangles are similar….

  • 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 that two triangles are similar….

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.


D that two triangles are similar….

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! that two triangles are similar….


A that two triangles are similar….

80

D

E

80

B

C

ABC ~ ADE by AA ~ Postulate


C that two triangles are similar….

6

10

D

E

5

3

A

B

CDE~ CAB by SAS ~ Theorem


L that two triangles are similar….

5

3

M

6

6

K

N

6

10

O

KLM~ KON by SSS ~ Theorem


A that two triangles are similar….

20

D

30

24

16

B

C

36

ACB~ DCA by SSS ~ Theorem


L that two triangles are similar….

15

P

A

25

9

N

LNP~ ANL by SAS ~ Theorem


Home work
Home Work that two triangles are similar….


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