Worksheets · Geometry
Parallelogram proofs worksheet Draw a diagonal and a parallelogram becomes two triangles, which is how every one of these proofs works. The definition gives you both pairs of opposite sides parallel, parallel lines give congruent alternate interior angles, the diagonal is shared so it is congruent to itself, and ASA finishes it. CPCTC then hands you whichever pair of opposite sides or angles you were asked for.
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Easy \egin{aligned}&\textbf{Given: } WXYZ \ ext{ is a parallelogram} \\&\textbf{Prove: } \angle XWY \cong \angle ZYW\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; WXYZ \ ext{ is a parallelogram} & \text{Given} \\\hline 2.\; \overline{WX} \parallel \overline{YZ} & \; \\\hline 3.\; \angle XWY \cong \angle ZYW & \; \\\hline\end{array} 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent Medium \egin{aligned}&\textbf{Given: } \overline{WX} \parallel \overline{YZ} \\ &\qquad\quad\; \overline{WX} \cong \overline{YZ} \\&\textbf{Prove: } \overline{XY} \cong \overline{WZ}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{WX} \parallel \overline{YZ} & \text{Given} \\\hline 2.\; \angle XWY \cong \angle ZYW & \text{Alternate interior angles of parallel lines are congruent} \\\hline 3.\; \overline{WX} \cong \overline{YZ} & \text{Given} \\\hline 4.\; \overline{WY} \cong \overline{WY} & \; \\\hline 5.\; \triangle WXY \cong \triangle YZW & \; \\\hline 6.\; \overline{XY} \cong \overline{WZ} & \; \\\hline\end{array} 4. Reflexive property 5. SAS 6. CPCTC 4. Reflexive property 5. SAS 6. CPCTC Hard \egin{aligned}&\textbf{Given: } \overline{WX} \parallel \overline{YZ} \\ &\qquad\quad\; \overline{WX} \cong \overline{YZ} \\&\textbf{Prove: } WXYZ \ ext{ is a parallelogram}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{WX} \parallel \overline{YZ} & \text{Given} \\\hline 2.\; \angle XWY \cong \angle ZYW & \text{Alternate interior angles of parallel lines are congruent} \\\hline 3.\; \overline{WX} \cong \overline{YZ} & \text{Given} \\\hline 4.\; \overline{WY} \cong \overline{WY} & \text{Reflexive property} \\\hline 5.\; \triangle WXY \cong \triangle YZW & \text{SAS} \\\hline 6.\; \angle XYW \cong \angle ZWY & \; \\\hline 7.\; \overline{XY} \parallel \overline{WZ} & \; \\\hline 8.\; WXYZ \ ext{ is a parallelogram} & \; \\\hline\end{array} 6. CPCTC 7. If alternate interior angles are congruent, the lines are parallel 8. If both pairs of opposite sides are parallel, the figure is a parallelogram 6. CPCTC 7. If alternate interior angles are congruent, the lines are parallel 8. If both pairs of opposite sides are parallel, the figure is a parallelogram
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Sigma Prep · sigmaprep.io/worksheets
Name
Parallelogram Proofs Date
Complete each proof.
A B C D \egin{aligned}&\textbf{Given: } \overline{AB} \parallel \overline{CD} \\ &\qquad\quad\; \overline{AB} \cong \overline{CD} \\&\textbf{Prove: } \overline{BC} \cong \overline{AD}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{AB} \parallel \overline{CD} & \text{Given} \\\hline 2.\; \angle BAC \cong \angle DCA & \text{Alternate interior angles of parallel lines are congruent} \\\hline 3.\; \overline{AB} \cong \overline{CD} & \; \\\hline 4.\; \overline{AC} \cong \overline{AC} & \; \\\hline 5.\; \triangle ABC \cong \triangle CDA & \text{SAS} \\\hline 6.\; \overline{BC} \cong \overline{AD} & \; \\\hline\end{array} R S T U \egin{aligned}&\textbf{Given: } \overline{RS} \parallel \overline{TU} \\ &\qquad\quad\; \overline{RS} \cong \overline{TU} \\&\textbf{Prove: } \overline{ST} \cong \overline{RU}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{RS} \parallel \overline{TU} & \; \\\hline 2.\; \angle SRT \cong \angle UTR & \; \\\hline 3.\; \overline{RS} \cong \overline{TU} & \; \\\hline 4.\; \overline{RT} \cong \overline{RT} & \; \\\hline 5.\; \triangle RST \cong \triangle TUR & \; \\\hline 6.\; \overline{ST} \cong \overline{RU} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Linear pairs are supplementary} \;\cdot\; \text{CPCTC} \;\cdot\; \text{If base angles are congruent, the triangle is isosceles} \;\cdot\; \text{All right angles are congruent} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Given} \;\cdot\; \text{Complements of congruent angles are congruent} \;\cdot\; \text{SAS} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} P Q R S \egin{aligned}&\textbf{Given: } PQRS \ ext{ is a parallelogram} \\&\textbf{Prove: } \overline{PQ} \cong \overline{RS}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; PQRS \ ext{ is a parallelogram} & \text{Given} \\\hline 2.\; \overline{PQ} \parallel \overline{RS} \text{ and } \overline{QR} \parallel \overline{PS} & \; \\\hline 3.\; \angle QPR \cong \angle SRP & \text{Alternate interior angles of parallel lines are congruent} \\\hline 4.\; \angle QRP \cong \angle SPR & \; \\\hline 5.\; \overline{PR} \cong \overline{PR} & \; \\\hline 6.\; \triangle PQR \cong \triangle RSP & \text{ASA} \\\hline 7.\; \overline{PQ} \cong \overline{RS} & \text{CPCTC} \\\hline\end{array} J K L M \egin{aligned}&\textbf{Given: } \overline{JK} \parallel \overline{LM} \\ &\qquad\quad\; \overline{JK} \cong \overline{LM} \\&\textbf{Prove: } \overline{KL} \cong \overline{JM}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{JK} \parallel \overline{LM} & \; \\\hline 2.\; \angle KJL \cong \angle MLJ & \; \\\hline 3.\; \overline{JK} \cong \overline{LM} & \; \\\hline 4.\; \overline{JL} \cong \overline{JL} & \; \\\hline 5.\; \triangle JKL \cong \triangle LMJ & \; \\\hline 6.\; \overline{KL} \cong \overline{JM} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{If alternate interior angles are congruent, the lines are parallel} \;\cdot\; \text{HL} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Given} \;\cdot\; \text{Base angles of an isosceles triangle are congruent} \;\cdot\; \text{CPCTC} \;\cdot\; \text{SAS} \;\cdot\; \text{Definition of a segment bisector} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} J K L M \egin{aligned}&\textbf{Given: } JKLM \ ext{ is a parallelogram} \\&\textbf{Prove: } \overline{JK} \cong \overline{LM}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; JKLM \ ext{ is a parallelogram} & \text{Given} \\\hline 2.\; \overline{JK} \parallel \overline{LM} \text{ and } \overline{KL} \parallel \overline{JM} & \; \\\hline 3.\; \angle KJL \cong \angle MLJ & \; \\\hline 4.\; \angle KLJ \cong \angle MJL & \text{Alternate interior angles of parallel lines are congruent} \\\hline 5.\; \overline{JL} \cong \overline{JL} & \text{Reflexive property} \\\hline 6.\; \triangle JKL \cong \triangle LMJ & \; \\\hline 7.\; \overline{JK} \cong \overline{LM} & \text{CPCTC} \\\hline\end{array} A B C D \egin{aligned}&\textbf{Given: } \overline{AB} \parallel \overline{CD} \\ &\qquad\quad\; \overline{AB} \cong \overline{CD} \\&\textbf{Prove: } \overline{BC} \cong \overline{AD}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{AB} \parallel \overline{CD} & \; \\\hline 2.\; \angle BAC \cong \angle DCA & \; \\\hline 3.\; \overline{AB} \cong \overline{CD} & \; \\\hline 4.\; \overline{AC} \cong \overline{AC} & \; \\\hline 5.\; \triangle ABC \cong \triangle CDA & \; \\\hline 6.\; \overline{BC} \cong \overline{AD} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Given} \;\cdot\; \text{CPCTC} \;\cdot\; \text{SAS} \;\cdot\; \text{Substitution} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} \;\cdot\; \text{If same-side interior angles are supplementary, the lines are parallel} \;\cdot\; \text{Definition of perpendicular} \;\cdot\; \text{AAS} \;\cdot\; \text{Reflexive property} K L M N \egin{aligned}&\textbf{Given: } \overline{KL} \parallel \overline{MN} \\ &\qquad\quad\; \overline{KL} \cong \overline{MN} \\&\textbf{Prove: } \overline{LM} \cong \overline{KN}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{KL} \parallel \overline{MN} & \text{Given} \\\hline 2.\; \angle LKM \cong \angle NMK & \; \\\hline 3.\; \overline{KL} \cong \overline{MN} & \; \\\hline 4.\; \overline{KM} \cong \overline{KM} & \text{Reflexive property} \\\hline 5.\; \triangle KLM \cong \triangle MNK & \text{SAS} \\\hline 6.\; \overline{LM} \cong \overline{KN} & \; \\\hline\end{array} W X Y Z \egin{aligned}&\textbf{Given: } \overline{WX} \parallel \overline{YZ} \\ &\qquad\quad\; \overline{WX} \cong \overline{YZ} \\&\textbf{Prove: } \overline{XY} \cong \overline{WZ}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{WX} \parallel \overline{YZ} & \; \\\hline 2.\; \angle XWY \cong \angle ZYW & \; \\\hline 3.\; \overline{WX} \cong \overline{YZ} & \; \\\hline 4.\; \overline{WY} \cong \overline{WY} & \; \\\hline 5.\; \triangle WXY \cong \triangle YZW & \; \\\hline 6.\; \overline{XY} \cong \overline{WZ} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Reflexive property} \;\cdot\; \text{SAS} \;\cdot\; \text{CPCTC} \;\cdot\; \text{Same-side interior angles of parallel lines are supplementary} \;\cdot\; \text{Angle addition postulate} \;\cdot\; \text{Given} \;\cdot\; \text{HL} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} \;\cdot\; \text{AAS}
Sigma Prep · sigmaprep.io/worksheets
Name
Parallelogram ProofsAnswer keyVersion 1 Date
Complete each proof.
A B C D \egin{aligned}&\textbf{Given: } \overline{AB} \parallel \overline{CD} \\ &\qquad\quad\; \overline{AB} \cong \overline{CD} \\&\textbf{Prove: } \overline{BC} \cong \overline{AD}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{AB} \parallel \overline{CD} & \text{Given} \\\hline 2.\; \angle BAC \cong \angle DCA & \text{Alternate interior angles of parallel lines are congruent} \\\hline 3.\; \overline{AB} \cong \overline{CD} & \; \\\hline 4.\; \overline{AC} \cong \overline{AC} & \; \\\hline 5.\; \triangle ABC \cong \triangle CDA & \text{SAS} \\\hline 6.\; \overline{BC} \cong \overline{AD} & \; \\\hline\end{array} 3. Given 4. Reflexive property 6. CPCTC 3. Given 4. Reflexive property 6. CPCTC R S T U \egin{aligned}&\textbf{Given: } \overline{RS} \parallel \overline{TU} \\ &\qquad\quad\; \overline{RS} \cong \overline{TU} \\&\textbf{Prove: } \overline{ST} \cong \overline{RU}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{RS} \parallel \overline{TU} & \; \\\hline 2.\; \angle SRT \cong \angle UTR & \; \\\hline 3.\; \overline{RS} \cong \overline{TU} & \; \\\hline 4.\; \overline{RT} \cong \overline{RT} & \; \\\hline 5.\; \triangle RST \cong \triangle TUR & \; \\\hline 6.\; \overline{ST} \cong \overline{RU} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Linear pairs are supplementary} \;\cdot\; \text{CPCTC} \;\cdot\; \text{If base angles are congruent, the triangle is isosceles} \;\cdot\; \text{All right angles are congruent} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Given} \;\cdot\; \text{Complements of congruent angles are congruent} \;\cdot\; \text{SAS} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC P Q R S \egin{aligned}&\textbf{Given: } PQRS \ ext{ is a parallelogram} \\&\textbf{Prove: } \overline{PQ} \cong \overline{RS}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; PQRS \ ext{ is a parallelogram} & \text{Given} \\\hline 2.\; \overline{PQ} \parallel \overline{RS} \text{ and } \overline{QR} \parallel \overline{PS} & \; \\\hline 3.\; \angle QPR \cong \angle SRP & \text{Alternate interior angles of parallel lines are congruent} \\\hline 4.\; \angle QRP \cong \angle SPR & \; \\\hline 5.\; \overline{PR} \cong \overline{PR} & \; \\\hline 6.\; \triangle PQR \cong \triangle RSP & \text{ASA} \\\hline 7.\; \overline{PQ} \cong \overline{RS} & \text{CPCTC} \\\hline\end{array} 2. Definition of a parallelogram 4. Alternate interior angles of parallel lines are congruent 5. Reflexive property 2. Definition of a parallelogram 4. Alternate interior angles of parallel lines are congruent 5. Reflexive property J K L M \egin{aligned}&\textbf{Given: } \overline{JK} \parallel \overline{LM} \\ &\qquad\quad\; \overline{JK} \cong \overline{LM} \\&\textbf{Prove: } \overline{KL} \cong \overline{JM}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{JK} \parallel \overline{LM} & \; \\\hline 2.\; \angle KJL \cong \angle MLJ & \; \\\hline 3.\; \overline{JK} \cong \overline{LM} & \; \\\hline 4.\; \overline{JL} \cong \overline{JL} & \; \\\hline 5.\; \triangle JKL \cong \triangle LMJ & \; \\\hline 6.\; \overline{KL} \cong \overline{JM} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{If alternate interior angles are congruent, the lines are parallel} \;\cdot\; \text{HL} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Given} \;\cdot\; \text{Base angles of an isosceles triangle are congruent} \;\cdot\; \text{CPCTC} \;\cdot\; \text{SAS} \;\cdot\; \text{Definition of a segment bisector} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC J K L M \egin{aligned}&\textbf{Given: } JKLM \ ext{ is a parallelogram} \\&\textbf{Prove: } \overline{JK} \cong \overline{LM}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; JKLM \ ext{ is a parallelogram} & \text{Given} \\\hline 2.\; \overline{JK} \parallel \overline{LM} \text{ and } \overline{KL} \parallel \overline{JM} & \; \\\hline 3.\; \angle KJL \cong \angle MLJ & \; \\\hline 4.\; \angle KLJ \cong \angle MJL & \text{Alternate interior angles of parallel lines are congruent} \\\hline 5.\; \overline{JL} \cong \overline{JL} & \text{Reflexive property} \\\hline 6.\; \triangle JKL \cong \triangle LMJ & \; \\\hline 7.\; \overline{JK} \cong \overline{LM} & \text{CPCTC} \\\hline\end{array} 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent 6. ASA 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent 6. ASA A B C D \egin{aligned}&\textbf{Given: } \overline{AB} \parallel \overline{CD} \\ &\qquad\quad\; \overline{AB} \cong \overline{CD} \\&\textbf{Prove: } \overline{BC} \cong \overline{AD}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{AB} \parallel \overline{CD} & \; \\\hline 2.\; \angle BAC \cong \angle DCA & \; \\\hline 3.\; \overline{AB} \cong \overline{CD} & \; \\\hline 4.\; \overline{AC} \cong \overline{AC} & \; \\\hline 5.\; \triangle ABC \cong \triangle CDA & \; \\\hline 6.\; \overline{BC} \cong \overline{AD} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Given} \;\cdot\; \text{CPCTC} \;\cdot\; \text{SAS} \;\cdot\; \text{Substitution} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} \;\cdot\; \text{If same-side interior angles are supplementary, the lines are parallel} \;\cdot\; \text{Definition of perpendicular} \;\cdot\; \text{AAS} \;\cdot\; \text{Reflexive property} 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC K L M N \egin{aligned}&\textbf{Given: } \overline{KL} \parallel \overline{MN} \\ &\qquad\quad\; \overline{KL} \cong \overline{MN} \\&\textbf{Prove: } \overline{LM} \cong \overline{KN}\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{KL} \parallel \overline{MN} & \text{Given} \\\hline 2.\; \angle LKM \cong \angle NMK & \; \\\hline 3.\; \overline{KL} \cong \overline{MN} & \; \\\hline 4.\; \overline{KM} \cong \overline{KM} & \text{Reflexive property} \\\hline 5.\; \triangle KLM \cong \triangle MNK & \text{SAS} \\\hline 6.\; \overline{LM} \cong \overline{KN} & \; \\\hline\end{array} 2. Alternate interior angles of parallel lines are congruent 3. Given 6. CPCTC 2. Alternate interior angles of parallel lines are congruent 3. Given 6. CPCTC W X Y Z \egin{aligned}&\textbf{Given: } \overline{WX} \parallel \overline{YZ} \\ &\qquad\quad\; \overline{WX} \cong \overline{YZ} \\&\textbf{Prove: } \overline{XY} \cong \overline{WZ}\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{WX} \parallel \overline{YZ} & \; \\\hline 2.\; \angle XWY \cong \angle ZYW & \; \\\hline 3.\; \overline{WX} \cong \overline{YZ} & \; \\\hline 4.\; \overline{WY} \cong \overline{WY} & \; \\\hline 5.\; \triangle WXY \cong \triangle YZW & \; \\\hline 6.\; \overline{XY} \cong \overline{WZ} & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Reflexive property} \;\cdot\; \text{SAS} \;\cdot\; \text{CPCTC} \;\cdot\; \text{Same-side interior angles of parallel lines are supplementary} \;\cdot\; \text{Angle addition postulate} \;\cdot\; \text{Given} \;\cdot\; \text{HL} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} \;\cdot\; \text{AAS} 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 6. CPCTC
Found a mistake on this sheet?
How to do these Given A B C D A BC D A B ‾ ≅ C D ‾ A B ≅ C D
Draw the diagonal AC, shared by both triangles. Both pairs of opposite sides are parallel, giving two pairs of alternate interior angles. ASA proves the triangles congruent, then CPCTC. The answer is CPCTC
Where students go wrong Assuming the property you are proving. If the question asks you to prove opposite sides congruent, you cannot start by saying they are congruent because it is a parallelogram.
Also called quadrilateral proofs, proving a quadrilateral is a parallelogram, opposite sides of a parallelogram or properties of parallelograms proof.
What you can put on this worksheet
Fill in the missing reasons \egin{aligned}&\textbf{Given: } WXYZ \ ext{ is a parallelogram} \\&\textbf{Prove: } \angle XWY \cong \angle ZYW\end{aligned} \\[4pt] \text{Give the missing reasons.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; WXYZ \ ext{ is a parallelogram} & \text{Given} \\\hline 2.\; \overline{WX} \parallel \overline{YZ} & \; \\\hline 3.\; \angle XWY \cong \angle ZYW & \; \\\hline\end{array} → 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent
Fill in every reason \egin{aligned}&\textbf{Given: } WXYZ \ ext{ is a parallelogram} \\&\textbf{Prove: } \angle XWY \cong \angle ZYW\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; WXYZ \ ext{ is a parallelogram} & \; \\\hline 2.\; \overline{WX} \parallel \overline{YZ} & \; \\\hline 3.\; \angle XWY \cong \angle ZYW & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Given} \;\cdot\; \text{Alternate interior angles of parallel lines are congruent} \;\cdot\; \text{Substitution} \;\cdot\; \text{Complements of congruent angles are congruent} \;\cdot\; \text{Definition of a parallelogram} \;\cdot\; \text{All radii of a circle are congruent} → 1. Given 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent 1. Given 2. Definition of a parallelogram 3. Alternate interior angles of parallel lines are congruent
Fill in the missing statements \egin{aligned}&\textbf{Given: } WXYZ \ ext{ is a parallelogram} \\&\textbf{Prove: } \angle XWY \cong \angle ZYW\end{aligned} \\[4pt] \text{Give the missing statements.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; WXYZ \ ext{ is a parallelogram} & \text{Given} \\\hline 2.\; \; & \text{Definition of a parallelogram} \\\hline 3.\; \; & \text{Alternate interior angles of parallel lines are congruent} \\\hline\end{array} → 2. W X ‾ ∥ Y Z ‾ 3. ∠ X W Y ≅ ∠ Z Y W 2. W X ∥ Y Z 3. ∠ X WY ≅ ∠ Z YW
Write the whole proof \egin{aligned}&\textbf{Given: } WXYZ \ ext{ is a parallelogram} \\&\textbf{Prove: } \angle XWY \cong \angle ZYW\end{aligned} \\[4pt] \text{Write the proof. It takes 3 lines.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \; & \; \\\hline 2.\; \; & \; \\\hline 3.\; \; & \; \\\hline\end{array} → 1. W X Y Z e x t i s a p a r a l l e l o g r a m Given 2. W X ‾ ∥ Y Z ‾ Definition of a parallelogram 3. ∠ X W Y ≅ ∠ Z Y W Alternate interior angles of parallel lines are congruent 1. W X Y Z e x t i s a p a r a ll e l o g r am Given 2. W X ∥ Y Z Definition of a parallelogram 3. ∠ X WY ≅ ∠ Z YW Alternate interior angles of parallel lines are congruent
Name the postulate that finishes the proof \egin{aligned}&\textbf{Given: } \ ext{circle } O \\ &\qquad\quad\; \overline{OY} \perp \overline{WX} at Z \\&\textbf{Prove: } \overline{WZ} \cong \overline{XZ}\end{aligned} \\[4pt] \text{Which postulate proves the triangles congruent?} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \ ext{circle } O & \text{Given} \\\hline 2.\; \overline{OY} \perp \overline{WX} \text{ at } Z & \text{Given} \\\hline 3.\; \angle OZW \text{ and } \angle OZX \text{ are right angles} & \text{Definition of perpendicular} \\\hline 4.\; \overline{OW} \cong \overline{OX} & \text{All radii of a circle are congruent} \\\hline 5.\; \overline{OZ} \cong \overline{OZ} & \text{Reflexive property} \\\hline 6.\; \triangle OZW \cong \triangle OZX & \; \\\hline\end{array} → HL Questions about these worksheets Are these parallelogram proofs worksheets free? + Yes. Every parallelogram proofs sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Do the parallelogram proofs worksheets come with an answer key? + Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Are these parallelogram proofs worksheets printable? + Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
What grade are these parallelogram proofs worksheets for? + Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Can I get a different version of the same parallelogram proofs worksheet? + Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
Is this a free alternative to Kuta Software for parallelogram proofs? + That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the parallelogram proofs questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Can I choose how hard the parallelogram proofs questions are? + Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
What kinds of question are on a parallelogram proofs worksheet? + You pick from 5: fill in the missing reasons, fill in every reason, fill in the missing statements, write the whole proof and name the postulate that finishes the proof. Tick as many as you want and set how many of each, or let it spread them evenly.
What do students get wrong with parallelogram proofs? + Assuming the property you are proving. If the question asks you to prove opposite sides congruent, you cannot start by saying they are congruent because it is a parallelogram.
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