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# 6.4 and 6.5 Congruent and Similar Triangles - PowerPoint PPT Presentation

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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Presentation Transcript
6.4 and 6.5Congruent and Similar Triangles

• 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.

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 )

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

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 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

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

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 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 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 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 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! 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 that two triangles are similar….