6 4 and 6 5 congruent and similar triangles
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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. 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
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

slide7
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
  • 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.

slide14
D

A

C

B

F

E

SAS Similarity Theorem

Idea for proof

slide16
A

80

D

E

80

B

C

ABC ~ ADE by AA ~ Postulate

slide17
C

6

10

D

E

5

3

A

B

CDE~ CAB by SAS ~ Theorem

slide18
L

5

3

M

6

6

K

N

6

10

O

KLM~ KON by SSS ~ Theorem

slide19
A

20

D

30

24

16

B

C

36

ACB~ DCA by SSS ~ Theorem

slide20
L

15

P

A

25

9

N

LNP~ ANL by SAS ~ Theorem

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