CPCTC Proof Practice
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Last updated about 1 year ago
7 questions
Explain how you can use SSS, SAS, ASA, or AAS along with CPCTC to prove each statement true.
***Note: Information provided on the diagram with congruence or other markings is "Given" information.
7
Given: \overline{AC}\perp\overline{BD}, \overline{AD}\cong\overline{CD}
Prove: \angle{A}\cong\angle{C}
Statement Reason
1. \overline{AC}\perp\overline{BD} __________
2. \overline{AD}\cong\overline{CD} __________
3. \angle{ADB} and \angle{CDB} are rt \angle's ________________________________
4. \angle{ADB}\cong\angle{CDB} ___________________________________
5. \overline{BD}\cong\overline{BD} _______________________
6. \triangle{ABD}\cong\triangle{CBD} ________
7. \angle{A}\cong\angle{C} __________
Other Answer Choices:
SAS
All right angles are congruent
AAS
symmetric property
congruence property
ASA
Vertical Angles are \cong
Given
SSS
CPCTC
Definition of perpendicular
Prove
Definition of Midpoint
reflexive property
Alternate Interior Angles
5
Given: \angle{EFH}\cong\angle{GHF}, \angle{EHF}\cong\angle{GFH}
Prove: \overline{HE}\cong\overline{FG}
Statement Reason
1. \angle{EFH}\cong\angle{GHF} __________
2. \angle{EHF}\cong\angle{GFH} __________
3. \overline{HF}\cong\overline{FH} _______________________
4. \triangle{EFH}\cong\triangle{GHF} ________
5. \overline{HE}\cong\overline{FG} __________
Other Answer Choices:
all right angles are congruent
ASA
Alternate Interior Angles
Given
SAS
Definition of Midpoint
Reflexive Property
Property of Shared Sides
Vertical Angles are \cong
Prove
SSS
AAS
Definition of Perpendicular
CPCTC
6
Given: Use Picture
Prove: \angle{K}\cong\angle{P}
Statement Reason
1. \angle{J}\cong\angle{N} __________
2. \angle{L} and \angle{M} are rt \angle's __________
3. \overline{JL}\cong\overline{NM} __________
4. \angle{L}\cong\angle{M} ___________________________________
5. \triangle{JLK}\cong\triangle{NMP} ________
6. \angle{K}\cong\angle{P} __________
Other Answer Choices:
SAS
Given
Alternate Interior Angles are \cong
Property of Shared Sides
SSS
all right angles are congruent
Definition of Midpoint
ASA
Reflexive Property
Prove
CPCTC
Vertical Angles are \cong
AAS
8
Given: Use Picture
Prove: \angle{QST}\cong\angle{SQR}
Statement Reason
1. \angle{TQS}\cong\angle{RSQ} __________
2. \angle{T} and \angle{R} are rt \angle's __________
3. \angle{T}\cong\angle{R} ___________________________________
4. ____________________________________ _______________________
5. \triangle{TQS}\cong\triangle{RSQ} ________
6. ________________________________ __________
Other Answer Choices:
Given
\overline{QS}\cong\overline{SQ}
\overline{QT}\cong\overline{SR}
Reflexive Property
All right angles are congruent
Alternate Interior Angles are \cong
\overline{QR}\cong\overline{ST}
SSS
AAS
Definition of Midpoint
Definition of perpendicular
Prove
ASA
Symmetric Property
SAS
\angle{QST}\cong\angle{SQR}
CPCTC
8
Given: Use Picture
Prove: \angle{U}\cong\angle{W}
Statement Reason
1. \overline{UV}\cong\overline{WV} __________
2. ____________________________________ __________
3. ____________________________________ _______________________
4. \triangle{TQS}\cong\triangle{RSQ} ________
5. ____________________________ __________
Other Answer Choices:
Reflexive Property
\angle{UVX}\cong\angle{WVX}
ASA
\angle{U}\cong\angle{W}
\angle{UXV}\cong\angle{WXV}
All right angles are congruent
AAS
Alternate Interior Angles are \cong
\overline{VX}\cong\overline{VX}
SSS
Given
CPCTC
Definition of Midpoint
Prove
SAS
Symmetric Property
\overline{UX}\cong\overline{WX}
Definition of perpendicular
8
Given: Use Picture
Prove: \overline{ZA}\cong\overline{CA}
Statement Reason
1. \overline{YA}\cong\overline{BA} __________
2. ____________________________ __________
3. ________________________________ ______________________________
4. \triangle{YZA}\cong\triangle{BCA} ________
5. ____________________________________ __________
Other Answer Choices:
Vertical Angles are \cong
\overline{YZ}\cong\overline{BC}
Reflexive Property
Alternate Interior Angles are \cong
Symmetric Property
All right angles are congruent
Prove
SAS
Definition of Midpoint
Given
CPCTC
SSS
\angle{ZAY}\cong\angle{CAB}
AAS
\angle{Z}\cong\angle{C}
\overline{ZA}\cong\overline{CA}
Definition of perpendicular
ASA
\angle{Y}\cong\angle{B}
10
Given: \overline{CB}\parallel\overline{ED}, \overline{CB}\cong\overline{ED}, C is the midpoint of \overline{AE}
Prove: \overline{AB}\parallel\overline{CD}
Statement Reason
1. \overline{CB}\parallel\overline{ED} __________
2. \overline{CB}\cong\overline{ED} __________
3. C is the midpoint of \overline{AE} __________
4. \overline{AC}\cong\overline{CE} ___________________________
5. ________________________________ ___________________________________
6. \triangle{ABC}\cong\triangle{CDE} ________
7. ________________________________ __________
8. \overline{AB}\parallel\overline{CD} ___________________________________
Other Answer Choices:
SSS
SAS
Definition of rt \angle
CPCTC
same side interior angles are \cong
Definition of congruent
\angle{CAB}\cong\angle{ECD}
Given
\angle{ACB}\cong\angle{CED}
alternate interior angles are \cong
AAS
\angle{B}\cong\angle{D}
corresponding angles are \cong
\overline{AB}\cong\overline{CD}
ASA
Definition of midpoint