CPCTC Proof Practice - HUGH DANIELS | Library

Instructions

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
\overline{AC}\perp\overline{BD}                                    __________    
\overline{AD}\cong\overline{CD}                                    __________ 
\angle{ADB} and \angle{CDB} are rt \angle's ________________________________ 
\angle{ADB}\cong\angle{CDB}                      ___________________________________ 
\overline{BD}\cong\overline{BD}                                     _______________________  
\triangle{ABD}\cong\triangle{CBD}                     ________ 
\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
\overline{CB}\parallel\overline{ED}                           __________ 
\overline{CB}\cong\overline{ED}                          __________ 
C is the midpoint of \overline{AE}  __________ 
\overline{AC}\cong\overline{CE}                          ___________________________    
________________________________               ___________________________________ 
\triangle{ABC}\cong\triangle{CDE}           ________ 
________________________________               __________ 
\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