ags station 1 name: proving triangles congruent: asa, aas...

AGS Station 1 name: _________________________

Proving Triangles Congruent: ASA, AAS, SAS, SSS date: __________________________

For each problem give the correct naming order of the congruent triangles. Write that name in order on the lines for the problem number (see box at bottom). Also, indicate which postulate or theorem is being used.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

___ ___ ___ ___ ___ _O_ ___ ___ _N_ ___ ___ ___ _S_ ___ ___ _E_ ___ _I_ ___ ___ ___ ___ ___ _T_ ___

4 4 4 8 8 8 12 12 12 2 2 2 5 5 5 9 9 9 6

___ ___ ___ _E_ _E_ ___ ___ ___ _O_ ___ ___ _N_ ___ _U_ ___ ___ ___ ___ _T_ ___ _E_ ___ ___ _I_ ___ .

6 6 10 10 10 1 1 1 3 3 3 7 7 7 11 11 11 (When you are done with the puzzle, there are: 3 SAS, 5 AAS, 2 ASA, and 2 SSS instances.)

W

A

B I

C R B

C G

A N B

A S

C E

G

J R

H E C

A E

B Y C

B S

A D

O

M K

N A

H T

A T H

C

B I

A L K

J T

L H D

F S

E N

H A A

B

C G

A K A

B Y

C D

P E S

ABC _______ by _________

ABC _______ by _________

ABC _______ by _________

ABC _______ by _________

GHJ _______ by _________

ABC _______ by _________

DEF _______ by _________

ABC _______ by _________

JKL _______ by _________

ABC _______ by _________

ABC _______ by _________

MNO _______ by _________

AGS Name: ____________________

Station 2: Triangle Congruence

a) Determine whether the following triangles are congruent

b) If they are, name the triangle congruence (pay attention to proper correspondence when

naming the triangles) and then identify the Theorem or Postulate (SSS, SAS, ASA, AAS, HL) that

supports your conclusion

c) Be sure to show any additional congruence markings you used in your reasoning

d) if the triangles cannot be proven congruent, state “not possible.”

Use the given information to mark the diagram appropriately. Name the triangle congruence

and then identify the theorem or postulate (SSS, SAS, ASA, AAS, HL) that would be used to

prove the triangles congruent.

Student Name: __________________________ Score:

Free Math Worksheets @ http://www.mathworksheets4kids.com

Write all the angles from the given angles:

Parallel Lines and Transversals Worksheet

Student Name: __________________________ Score:

Free Math Worksheets @ http://www.mathworksheets4kids.com

Answers

ANSWER KEY

J. Yes, SSS K. Not Similar L. Yes, SAS M. Yes, AA

N. Not Similar O. Yes, SSS P. Yes, SAS Q. Yes, AA

K.Yes, SAS L. Yes, SSS M. Yes, AA N. Not Similar

L. Yes, SAS M. Yes, SSS N. Not Similar O. Yes, AA

P. Yes, SSS Q. Yes, AA R. Yes, SAS S. Not Similar

P. Not Similar Q. Yes, SSS R. Yes, SAS S. Yes, AA

D. Yes, AA E. Not Similar F. Yes, SAS G. Yes, SSS

B. Not Similar C. Yes, SSS D. Yes, AA E. Yes, SAS

W. Not Similar X. Yes, SAS Y. Yes, SSS Z. Yes, AA

O. Yes, SSS P. Yes, ASA Q. Not Similar R. Yes, AA

L. Not Similar M. Yes, SSS N. Yes, AA O. Yes, SAS

E. Yes, AA F. Yes, SAS G. Not Similar H. Yes, SSS

What was the blackbird doing in the school

library?

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Determine whether each set of triangles is similar and why.

J. Yes, SSS K. Not Similar L. Yes, SAS M. Yes, AA

N. Not Similar O. Yes, SSS P. Yes, SAS Q. Yes, AA

K.Yes, SAS L. Yes, SSS M. Yes, AA N. Not Similar

L. Yes, SAS M. Yes, SSS N. Not Similar O. Yes, AA

P. Yes, SSS Q. Yes, AA R. Yes, SAS S. Not Similar

P. Not Similar Q. Yes, SSS R. Yes, SAS S. Yes, AA

D. Yes, AA E. Not Similar F. Yes, SAS G. Yes, SSS

B. Not Similar C. Yes, SSS D. Yes, AA E. Yes, SAS

W. Not Similar X. Yes, SAS Y. Yes, SSS Z. Yes, AA

O. Yes, SSS P. Yes, ASA Q. Not Similar R. Yes, AA

L. Not Similar M. Yes, SSS N. Yes, AA O. Yes, SAS

E. Yes, AA F. Yes, SAS G. Not Similar H. Yes, SSS

What was the blackbird doing in the school library?

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11) R Q

EF

D

DDEF ~ ______

12)

8

9

B

C

16

18

Q

RP

DPQR ~ ______

13)

S

T

F

GE

DEFG ~ ______

14)

42

33 21

UV

W

56

44 28

LM

N

DLMN ~ ______

15)

10

9

D

E

20

18

V

W

U

DUVW ~ ______

16)

18

24

G

H60

80

V

W

U

DUVW ~ ______

-3-

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17) 8

7

14

LK

J

24 21

39U

V

W

DUVW ~ ______

18) Q

PF

E

G

DGFE ~ ______

19)

24

22

F

G

36

33

L

M

K

DKLM ~ ______

20)

40

10

37

5314

LM

N

27

H

G

DLMN ~ ______

21)

36

43

54°KB

C

8498 54°

K

LM

DKLM ~ ______

22)

28

18

22

L

KJ

98

63

77

Q

R S

DQRS ~ ______

-4-


29)

F

GL

M

K

DKLM ~ ______

30)

11 12

8M

L

K

22

24

16

D

CB

DDCB ~ ______

31)

68°

44°

F

MN

65°

47°

F

G

H

DFGH ~ ______

32)

27

17

C

D

63

36

M

L

N

DNML ~ ______

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45)

121

110

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K

L

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F

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3541

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H

71

84

96

S

RQ

DSRQ ~ ______

47)

67°

RS

T

68°

N

M

DRST ~ ______

48)

50 45

35F

B

C

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G

H

DFGH ~ ______

49)

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M

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30)

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L

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22

24

16

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DDCB ~ ______

31)

68°

44°

F

MN

65°

47°

F

G

H

DFGH ~ ______

32)

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17

C

D

63

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N

DNML ~ ______

-6-


Proving Triangles Similar

By Caryn White

Table of Contents Instructions Page ..................................................................................................................................................................... 3

Sort: All can be proven similar ................................................................................................................................................ 4

Flash Cards Back (reverse order for front to back printing) ................................................................................................... 5

Includes Triangles with not enough info to prove similar ...................................................................................................... 6

Flash Cards Back ...................................................................................................................................................................... 7

Student Answer Sheet – Version A ......................................................................................................................................... 8

Student Answer Sheet – Version B ......................................................................................................................................... 9

Pocket for sort ....................................................................................................................................................................... 10

Keys ....................................................................................................................................................................................... 11

The original purchaser of this document is granted permission to copy for teaching purposes only.

School - Wide use is permitted. An item may be edited for classroom use but not for the purpose of selling. Redistributing, editing, selling, and posting this item or any part thereof on the Internet are strictly prohibited without

first gaining permission from the author. Violations are subject to the penalties of the Digital Millennium Copyright Act. Please contact me if you wish to be granted special permission.

www.teacherspayteachers.com/Store/Caryn-Loves-Math

http://www.teacherspayteachers.com/Store/Caryn-Loves-Math

http://www.teacherspayteachers.com/Store/Caryn


Instructions Page

As a Sort

There are 24 cards. Depending on your needs you can use 12, 18, or all 24 cards. The 12 and 18 cards sets are

all triangles that can be proven similar. The 24 card set includes triangles that do have enough information to prove or

there is something incorrect (sides are not proportional).

I have included an answer sheet for student to record their results. This makes it easier to walk around and

check their work.

A key is proved for all forms of the sort.

Differentiation

This activity has been designed to allow for differentiation. Students that are struggling or have learning

difficulties can be given the shorter version (12 cards). While the average student plays the 18 card set and the

advanced learner can be given the 24 set.

As Flash Cards:

Print the cards and the answers front to back. I laminate mine for extended use. Students can then quiz each

other during class.

For Interactive Math Notebook (or Math Journal)

I print the sort on colored sheets. Students cut out the square and decide which method can be used to prove

the 2 triangles are similar. I have included a pocket for student to place their place cards in. Student glue the pocket

into their math notebook and place the flash card in it for later practice.

Possible Uses:

Bellwork

Check for understanding

Alternative to Homework

Extra Practice

Activity for interactive notebook


Sort: All can be proven similar

1 20 3

4 5

7 8

10 11 12

18

19


Flash Cards Back (reverse order for front to back printing)

AA~ AA~ SAS~

SSS~ SAS~ SAS~

AA~ SSS~ AA~

SSS~ SSS~ SAS~


Includes Triangles with not enough info to prove similar

6

9

13

14

15

16 17

2

21

22

23

24


Flash Cards Back

SSS~ AA~ SSS~

SAS~ SAS~ AA~

Not

Similar

Not

Similar

Not

Similar

Not

Similar

Not

Similar

Not

Similar


Student Answer Sheet – Version A Name ____________________

Period _______

First complete the sort by decided which theorem or postulate can you used to prove the triangles are similar Then list

the number of the card below.

AA~ SAS~ SSS~

Name ____________________

Period _______



AA~ SAS~ SSS~

Name ____________________

Period _______



AA~ SAS~ SSS~


Student Answer Sheet – Version B Name ____________________

Period _______



AA~ SAS~ SSS~ Can’t prove similarity

Name ____________________

Period _______




Name ____________________

Period _______





Pocket for sort


Keys

Key to sort using only first 12 cards

AA~

3,7,18,20

SAS~

1,4,5,10

SSS~

8,11,19,12

Key to sort using only first 18 cards

AA~

3,7,16,18,20,23

SAS~

1,4,5,10,17,21

SSS~

8,11,13,15,19,12

Key using all 24 cards

AA~

3,7,16,18,20,23

SAS~

1,4,5,10,17,21

SSS~

8,11,13,15,19,12

Can’t prove similarity

2,6,9,14,22,24


Credits Page

All graphs were designed by Caryn White

Backgrounds were designed by …

Thanks for your purchase.

Caryn White www.teacherspayteachers.com/Store/Caryn-Loves-Math

http://www.teacherspayteachers.com/Store/Ashley-Hughes-38

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AGS Name___________________________________

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Solve for

x.

1) 20

x − 1

15

6

2)

3

x − 3

2

3 1

3)

10

x − 4 2

7

4)

3

x + 1114

15

6

5)

14

5

x − 38

24

6)

x − 3

9

28

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2 +

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35

4

10

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AGS Name___________________________________

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Find the coordinates of the vertices of each figure with the origin as the center of dilation.

1) dilation of 2U(−1, −2), C(1, 2), L(2, −2)

2) dilation of 2.5L(−1, −1), P(1, 2), H(0, −2)

3) dilation of 0.5

x

y

A

R

E

4) dilation of 2

x

y

A

T F

Q

Graph the image of the figure with the origin as the center of dilation.

5) dilation of 2V(−1, 0), L(1, 2), D(1, −2)

x

y

6) dilation of 0.5H(−2, −2), I(0, 2), Z(3, 0), N(2, −2)

x

y

-1-

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7) dilation of 1.5V(0, −2), G(−2, 1), M(2, 2), I(3, −2)

x

y

8) dilation of 2W(−1, 1), B(1, 2), T(2, −1)

x

y

Write a rule to describe each transformation.

9)

x

y

V

W R

G

V'

W' R'

G'

10)

x

y

E

T

ME'

T'

M'

Dilate the following figures with the specified point as the center.

11) Triangle ABC has vertices A(7, 4), B(5, 0) and C(4, 2) by a scale factor of two, centered at thepoint (9, 2)

x

y

−10 −8 −6 −4 −2 2 4 6 8 10

−10

−8

−6

−4

−2

2

4

6

8

10

12) Triangle ABC has vertices A(8, -3), B(-6, -1)and C(0, 7) by a scale factor of ½, centered atpoint C.

x

y

−10 −8 −6 −4 −2 2 4 6 8 10

−10

−8

−6

−4

−2

2

4

6

8

10

-2-

ags station 1 name: proving triangles congruent: asa, aas...

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