Geometry CP – Ch 4 Test A Student



Geometry CP – Problem Set 4 Student _________________

Congruent Triangles

Use a cover sheet to cover your work. Put your final

answers in the blanks provided. Use correct symbols.

Classify the triangle by its angles AND by its sides.

Write a capital letter in each blank.

A) acute B) equilateral C) isosceles

D) obtuse E) right F) scalene

1. 2. 3.

4. 5. 6.

Given that [pic]ABC[pic][pic]RST, complete the following.

7.[pic]C [pic] ____ 8.[pic]A[pic] ____ 9.[pic][pic] ____ 10.[pic][pic] ____

In the diagram at the right, [pic]GFH [pic][pic]MLN.

11. Find MN.

12. Find GF.

13. Find m[pic]N.

14. Find m[pic]G.

Use the diagram at the right to complete the congruence statements for the given triangles.

15. [pic]C [pic] ____

16. DB[pic] ____

17. [pic]CBD[pic] ____

Find x.

18. 19.

20. 21.

Mark the given information on the triangles. What additional

information would you need to use the Congruence Postulate or

Theorem given to show [pic]ABC [pic][pic]XYZ ?

22. [pic], [pic] 23. [pic], [pic]A [pic][pic]X

SSS Congruence SAS Congruence

24. [pic]C [pic][pic]Z , [pic] 25. [pic]B [pic][pic]Y , [pic]

AAS Congruence ASA Congruence

Find x.

26. 27. 28.

29. 30.

Decide whether it is possible to prove that the triangles are congruent. If it is not possible with the given information, circle “not possible.” If it is possible, tell which congruence postulate or theorem you would use.

33. 34.

35. 36.

37. 38.

Complete the proof.

39. Given: WX || ZY , WZ || XY

Prove: (WXZ ( (YZX

|Statements |Reasons |

|1) WX || ZY , WZ || XY |1) Given |

|2) |2) |

|3) |3) |

|4) (WXZ ( (YZX |4) |

40. Given: AC ( DE , (C ( (D

Prove: (ABC ( (EBD

|Statements |Reasons |

|1) AC ( DE , (C ( (D |1) Given |

|2) |2) |

|3) (ABC ( (EBD |3) |

41. Given:

Prove:

|Statements |Reasons |

|1) |1) Given |

|2) |2) |

|3) |3) |

|4) |4) |

42. Given: AD ( CB, AD ( AB , BC ( DC

Prove: (ABD ( (CDB

|Statements |Reasons |

|1) AD ( CB, AD ( AB , BC ( DC |1) Given |

|2) (1 and (6 are _______________ |2) |

|3) (ABD and (CDB are ____________ |3) |

|4) BD ( BD |4) |

|5) (ABD ( (CDB |5) |

|Statements |Reasons |

|1) E is the midpoint of BC |1) Given |

|E is the midpoint of AD | |

|2) BE ( EC , AE ( ED |2) |

|3) (AEB ( (DEC |3) |

|4) [pic]AEB [pic] [pic]DEC |4) |

| |5) |

|5) AB ( C D | |

43. Given: E is the midpoint of BC

E is the midpoint of AD

Prove: AB ( C D

-----------------------

1. _____ _____

2. _____ _____

3. _____ _____

4. _____ _____

5. _____ _____

6. _____ _____

7. _____ 8. _____

9. _____ 10. _____

11. _____ 12. _____

13. _____ 14. _____

15. _____ 16. _____

17. ____________

18. ____________

19. ____________

20. ____________

21. ____________

41°

110°

89°

A

B

C

x°

30°

40°

Z

Y

X

C

B

A

Z

Y

X

C

B

A

Z

Y

X

C

B

A

4

5

1

3

1

6

4

3

D

C

B

A

33. Not possible

[pic]MNR[pic][pic]______

by ______

34. Not possible

[pic]ABC [pic][pic]______

by ______

35. Not possible

[pic]ABD[pic][pic]______

by ______

36. Not possible

[pic]ABC[pic][pic]______

by ______

37. Not possible

[pic]BCD[pic][pic]______

by ______

38. Not possible

[pic]EDC [pic][pic]______

by ______

A

B

C

D

E

X

W

Z

Y

A

M

75°

B

C

D

N

P

R

A

B

D

E

C

C

E

D

B

A

Z

Y

22. ____________

23. ____________

24. ____________

25. ____________

26. ____________

27. ____________

28. ____________

29. ____________

30. ____________

X

x°

x°

x°

70°

50°

30°

30°

[pic]

5

[pic]

2

3

4

2

6

1

2

[pic]

[pic]

6

5

4

1

6

5

4

1

2

3

2

3

+

-

+ 5

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