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Name _____________________________________ Date ________ Per. ____ Ms. Williams/Mrs. Hertel
REVIEW FOR CONGRUENT TRIANGLES TEST
Level A Honor Proofs
1.
2.
3.
Level B Honor Proofs
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Level C Honor Proof
15.
16. The segments drawn from the midpoint of the base of an isosceles triangle to the midpoints of the
legs are congruent.
17. Given: ,
Prove: bisects RPS
Q
P
T U
SR
Answer Key:
1.
Statements Reasons
1. Quadrilateral ABCD, AFEC 1. Given
2. , 2. Given
3. , 3. Given
4. 4. Reflexive Property
5. ADC CBA 5. SSS (2, 2, 4)
6. DAC BCA 6. CPCTC
7. DFA and BEC are right angles 7. Def of perpendicular lines
8. DFA BEC 8. Right angles are congruent
9. AFD CEB 9. AAS (6, 8, 2)
10. 10. CPCTC
2.
Statements Reasons
1. ABC, is median and altitude to 1. Given
2. D is the midpoint of 2. Def of median
3. 3. Def of midpoint
4. 4. Def of altitude
5. ADB and CDB are right angles 5. Def of Perpendicular Lines
6. ADB CDB 6. Right angles are congruent
7. 7. Reflexive Property
8. ADB CDB 8. SAS (3, 6, 7)
9. 9. CPCTC
3.
Statements Reasons
1. 1 5, 2 6 1. Given
2. 1 + 2 5 + 6 2. Addition Postulate
3. DBA ECA 3. Substitution Postulate
5. DBA supp 3; ECA supp 4 5. Linear Pair Theorem
6. 3 4 6. Congruent Supplements Theorem
7. ABC is isosceles 7. If the base angles of a triangle are congruent, the triangle is isosceles.
4.
5.
6. Statements Reasons
1. O, 1. Given
2. 2. All radii of a circle are congruent.
3. DOB EOA 3. Given
4. DOE DOE 4. Reflexive Property
5. DOB - DOE AOE - DOE 5. Subtraction Postulate
6. AOD EOB 6. Substitution
7. AOD BOE 7. SAS (1, 6, 2)
8. A B 8. CPCTC
9.
9.
10. 10. CPCTC
11. – - 11. Subtraction Postulate
12. 12. Substitution
7.
8.
9. Given: APB with perpendicular bisector
Prove:
Statements Reasons
1. APB with perpendicular bisector 1. Given
2. M is the midpoint of 2. Def of segment bisector
3. 3. Def of midpoint
4. AMP and BMP are right angles 4. Def of perpendicular lines
5. AMP BMP 5. Right angles are congruent
6. 6. Reflexive Property
7. ARM BRM 7. SAS (3, 5, 6)
8. 8. CPCTC
P
A BM
R
10.
11.
12.
13.
14.
15.
Statements Reasons
1. ABC is isosceles with base 1. Given
2. 2. Definition of Isosceles Triangles
3. ACB ABC
3.
4. is a median and is a median 4. Given
5. D is the midpoint of and M is the midpoint of 5. Def of median
6. ½ ; = ½ 6. Def of midpoint
7. 7. Halves of congruent line segments are congruent. (Division Postulate)
8. 8. Reflexive Property
9. DCB MBC 9. SAS (7, 3, 8)
10. CDB BMC; 10. CPCTC
11. DEC MEB 11. Vertical angles are congruent
12. DCE MBE 12. AAS (10, 11, 7)
13. 13. CPCTC
14. – - 14. Subtraction
15. 15. Substitution
16. 16. If two points are equidistant from the endpoints of a line segment, they determine the perpendicular bisector of that segment. or Equidistance Thm (2, 15)
16. Given: ABC is isosceles with base BC, X, Y, M are midpoints of , , and , respectively.
Prove:
Statements Reasons
1. ABC is isosceles with base 1. Given
2. 2. Definition of Isosceles Triangles
3. X, Y, and M are midpoints of , , , respectively
3. Given
4. ½ ; ½ 4. Def of midpoint
5. 5. Halves of congruent line segments are congruent. (Division Postulate)
6. B C
6.
7. 7. Def of midpoint
8. XBM YCM 8. SAS (5, 6, 7)
9. 9. CPCTC
17.
A
B CM
X Y
