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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 :

6.4 and 6.5 Congruent and Similar Triangles

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### 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 :

• SSS ( Side – Side – Side )

• SAS ( Side – Angle – Side )

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

• RHS ( Right angle – Hypotenuse – Side )

### Thinking Time ?????

• 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

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

• 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

• 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

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

D

A

C

B

F

E

### 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

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

A

C

B

F

E

SAS Similarity Theorem

Idea for proof

A

80

D

E

80

B

C

ABC ~ ADE by AA ~ Postulate

C

6

10

D

E

5

3

A

B

CDE~ CAB by SAS ~ Theorem

L

5

3

M

6

6

K

N

6

10

O

KLM~ KON by SSS ~ Theorem

A

20

D

30

24

16

B

C

36

ACB~ DCA by SSS ~ Theorem

L

15

P

A

25

9

N

LNP~ ANL by SAS ~ Theorem