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CPCTC Proof Practice
By HUGH DANIELS
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Last updated over 1 year ago
7 questions
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Instructions
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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.
Question 1
1.
Other Answer Choices:
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SAS
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All right angles are congruent
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AAS
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symmetric property
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congruence property
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ASA
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Given
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SSS
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CPCTC
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Definition of perpendicular
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Prove
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Definition of Midpoint
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reflexive property
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Alternate Interior Angles
Question 2
2.
Other Answer Choices:
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all right angles are congruent
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ASA
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Alternate Interior Angles
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Given
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SAS
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Definition of Midpoint
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Reflexive Property
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Property of Shared Sides
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Prove
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SSS
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AAS
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Definition of Perpendicular
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CPCTC
Question 3
3.
Other Answer Choices:
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SAS
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Given
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Property of Shared Sides
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SSS
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all right angles are congruent
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Definition of Midpoint
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ASA
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Reflexive Property
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Prove
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CPCTC
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AAS
Question 4
4.
Other Answer Choices:
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Given
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Reflexive Property
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All right angles are congruent
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SSS
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AAS
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Definition of Midpoint
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Definition of perpendicular
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Prove
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ASA
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Symmetric Property
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SAS
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CPCTC
Question 5
5.
Other Answer Choices:
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Reflexive Property
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ASA
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All right angles are congruent
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AAS
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SSS
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Given
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CPCTC
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Definition of Midpoint
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Prove
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SAS
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Symmetric Property
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Definition of perpendicular
Question 6
6.
Other Answer Choices:
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Reflexive Property
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Symmetric Property
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All right angles are congruent
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Prove
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SAS
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Definition of Midpoint
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Given
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CPCTC
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SSS
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AAS
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Definition of perpendicular
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ASA
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Question 7
7.
Other Answer Choices:
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SSS
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SAS
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CPCTC
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Definition of congruent
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Given
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AAS
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ASA
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Definition of midpoint
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} __________
Vertical Angles are \cong
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} __________
Vertical Angles are \cong
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} __________
Alternate Interior Angles are \cong
Vertical Angles are \cong
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. ________________________________ __________
\overline{QS}\cong\overline{SQ}
\overline{QT}\cong\overline{SR}
Alternate Interior Angles are \cong
\overline{QR}\cong\overline{ST}
\angle{QST}\cong\angle{SQR}
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. ____________________________ __________
\angle{UVX}\cong\angle{WVX}
\angle{U}\cong\angle{W}
\angle{UXV}\cong\angle{WXV}
Alternate Interior Angles are \cong
\overline{VX}\cong\overline{VX}
\overline{UX}\cong\overline{WX}
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. ____________________________________ __________
Vertical Angles are \cong
\overline{YZ}\cong\overline{BC}
Alternate Interior Angles are \cong
\angle{ZAY}\cong\angle{CAB}
\angle{Z}\cong\angle{C}
\overline{ZA}\cong\overline{CA}
\angle{Y}\cong\angle{B}
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} ___________________________________
Definition of rt \angle
same side interior angles are \cong
\angle{CAB}\cong\angle{ECD}
\angle{ACB}\cong\angle{CED}
alternate interior angles are \cong
\angle{B}\cong\angle{D}
corresponding angles are \cong
\overline{AB}\cong\overline{CD}