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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