Congruent Triangles Study Guide - Central Bucks School District

[Pages:8]Geo/Trig Ch 4 ? Congruent Triangles Study Guide

Name: _________________________________ Date: ___________________________

I. Are the triangles congruent?

1. Determine if the triangles are congruent by SSS, SAS, ASA, AAS, or HL. If the triangles CANNOT be

proven congruent, write NONE for the reason.

1.

2.

3.

Reason: ______________________ 4.

Reason: _______________________ 5.

Reason: _____________________ 6.

Reason: ______________________ 7.

Reason: ______________________ 8.

Reason: ______________________ 9.

Reason: ______________________

Reason: ______________________

Reason: ______________________

II. Are the triangles congruent? Complete the triangle congruence statement.

1. Determine if the triangles are congruent by SSS, SAS, ASA, AAS, or HL. If the triangles CANNOT be

proven congruent, write NONE for the reason.

2. If the triangles are congruent, complete the congruence statement with the name of the second

triangle. Make sure the letters are in the correct order. If the triangles are NOT congruent write NONE.

10.

11.

12.

Reason: ______________________ ________________

Reason: ______________________ ________________

Reason: ______________________ ________________

13.

14.

15.

Reason: ______________________

________________ 16.

Reason: ______________________

________________ 17.

Reason: ______________________

________________ 18.

Reason: ______________________

________________ 19.

Reason: ______________________

________________ 20.

Reason: ______________________

________________ 21.

Reason: ______________________

Reason: ______________________

Reason: ______________________

________________

________________

________________

III. Apply given info. Are the triangles congruent? Complete the triangle congruence statement.

1. Determine if the triangles are congruent by SSS, SAS, ASA, AAS, or HL by applying the given

information. If the triangles CANNOT be proven congruent, write NONE for the reason.

2. If the triangles are congruent, complete the congruence statement with the name of the second

triangle. Make sure the letters are in the correct order.

22. Y is the midpoint of

23.

24. ||

Reason: ______________________ ________________

Reason: ______________________ _______________

Reason: ______________________ ________________

25. Hint: Apply the Base s Thm. 26. S is the midpoint of

27.

Reason: ______________________

________________

28. ||; ||

Reason:

_________________

________________

29.

Reason: ______________________

________________ 30.

Reason: ______________________ ________________

31. ;

Reason: ______________________ ________________

32. ; ;

Reason: ______________________ ________________

33. ;

Reason: ______________________ ________________

34. and bisect each

Reason: ______________________

________________ 35. bisects EGF;

Reason: ______________________

________________ 36. C is the midpoint of ;

other Reason: ______________________

________________

Reason: ______________________ ________________

Reason: ______________________ ________________

IV. Proofs ? will need to do on separate page.

1. Given: DF bisects EDG; DE DG Prove: E G

2. Given: ; Prove:

3. Given: AB CB

4.

BD bisects ABC

Prove: BD bisects AC

5. G: A & C are rt s

6.

AD BC

P: AD || BC

7. Given: AD CD

8.

BD bisects CDA

Prove: ABD & DBC are rt angles

V. Given two congruent segments, name two congruent angles.

X

X

1.

2.

3.

4.

________ ________

________ ________

________ ________

________ ________

What theorem are you applying in all of these problems? ____________________________________________________________

VI. Given two congruent angles name the two congruent segments.

5.

6.

7.

8.

________ ________

________ ________

________ ________

________ ________

What theorem are you applying in all of these problems? ___________________________________________________________

VII. Solve for x.

9.

10.

11.

12. Hint: the two triangles

13.

are congruent by SSS.

14.

15.

16.

17.

18. Given: ; 2; 1 Prove: is isosceles

19. Given: bisects ; Prove: is isosceles

VIII. Definition Details 20. Can a scalene triangle be a right triangle? ______ 21. Can an isosceles triangle be obtuse? _______ 22. Can an equiangular triangle be obtuse? _______ 23. Can an acute triangle be isosceles? _________ 24. Can a right triangle be obtuse? ________ 25. Can an isosceles triangle be equilateral? ______ 26. Can a triangle with 2 congruent angles be scalene? _______

IX. Angle Measures and Algebra Connections

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