Worksheets · Geometry
Proving triangles congruent worksheet Every one of these proofs ends the same way: line up three matching parts in the right pattern and name the postulate. The work is getting those three parts. A shared side is congruent to itself by the reflexive property, a midpoint splits a segment into two congruent halves, vertical angles are congruent, and parallel lines hand you congruent alternate interior angles. Collect three, check the pattern, and write SSS, SAS, ASA, AAS or HL.
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Easy \egin{aligned}&\textbf{Given: } \overline{PQ} \cong \overline{RQ} \\ &\qquad\quad\; \overline{QS} is a median of \overline{PR} \\&\textbf{Prove: } \triangle PQS \cong \triangle RQS\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{PQ} \cong \overline{RQ} & \text{Given} \\\hline 2.\; \overline{QS} \text{ is a median of } \overline{PR} & \; \\\hline 3.\; \overline{PS} \cong \overline{RS} & \; \\\hline 4.\; \overline{QS} \cong \overline{QS} & \text{Reflexive property} \\\hline 5.\; \triangle PQS \cong \triangle RQS & \text{SSS} \\\hline\end{array} 2. Given 3. Definition of a median 2. Given 3. Definition of a median Medium \egin{aligned}&\textbf{Given: } \overline{PQ} \cong \overline{RQ} \\ &\qquad\quad\; \overline{QS} \perp \overline{PR} \\&\textbf{Prove: } \triangle PQS \cong \triangle RQS\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{QS} \perp \overline{PR} & \text{Given} \\\hline 2.\; \angle QSP \text{ and } \angle QSR \text{ are right angles} & \; \\\hline 3.\; \angle QSP \cong \angle QSR & \; \\\hline 4.\; \overline{PQ} \cong \overline{RQ} & \text{Given} \\\hline 5.\; \overline{QS} \cong \overline{QS} & \; \\\hline 6.\; \triangle PQS \cong \triangle RQS & \text{HL} \\\hline\end{array} 2. Definition of perpendicular 3. All right angles are congruent 5. Reflexive property 2. Definition of perpendicular 3. All right angles are congruent 5. Reflexive property Hard \egin{aligned}&\textbf{Given: } \overline{WX} \parallel \overline{YZ} \\ &\qquad\quad\; \overline{XY} \parallel \overline{WZ} \\&\textbf{Prove: } \triangle WXY \cong \triangle YZW\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{XY} \parallel \overline{WZ} & \text{Given} \\\hline 4.\; \angle XYW \cong \angle ZWY & \; \\\hline 5.\; \overline{WY} \cong \overline{WY} & \; \\\hline 6.\; \triangle WXY \cong \triangle YZW & \; \\\hline\end{array} 4. Alternate interior angles of parallel lines are congruent 5. Reflexive property 6. ASA 4. Alternate interior angles of parallel lines are congruent 5. Reflexive property 6. ASA
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Sigma Prep · sigmaprep.io/worksheets
Name
Proving Triangles Congruent Date
Complete each proof.
A B C D \egin{aligned}&\textbf{Given: } \overline{AC} bisects \angle BCD \\ &\qquad\quad\; \overline{BC} \cong \overline{DC} \\&\textbf{Prove: } \triangle ABC \cong \triangle ADC\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{AC} \text{ bisects } \angle BCD & \text{Given} \\\hline 2.\; \angle BCA \cong \angle DCA & \text{Definition of an angle bisector} \\\hline 3.\; \overline{BC} \cong \overline{DC} & \; \\\hline 4.\; \overline{AC} \cong \overline{AC} & \; \\\hline 5.\; \triangle ABC \cong \triangle ADC & \; \\\hline\end{array} R S T U \egin{aligned}&\textbf{Given: } \overline{RT} bisects \angle STU \\ &\qquad\quad\; \overline{ST} \cong \overline{UT} \\&\textbf{Prove: } \triangle RST \cong \triangle RUT\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{RT} \text{ bisects } \angle STU & \; \\\hline 2.\; \angle STR \cong \angle UTR & \; \\\hline 3.\; \overline{ST} \cong \overline{UT} & \; \\\hline 4.\; \overline{RT} \cong \overline{RT} & \; \\\hline 5.\; \triangle RST \cong \triangle RUT & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{SAS} \;\cdot\; \text{Supplements of congruent angles are congruent} \;\cdot\; \text{Linear pairs are supplementary} \;\cdot\; \text{If base angles are congruent, the triangle is isosceles} \;\cdot\; \text{Given} \;\cdot\; \text{Base angles of an isosceles triangle are congruent} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Definition of an angle bisector} J K L M \egin{aligned}&\textbf{Given: } \overline{JK} \cong \overline{LK} \\ &\qquad\quad\; \overline{KM} \perp \overline{JL} \\&\textbf{Prove: } \triangle JKM \cong \triangle LKM\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{KM} \perp \overline{JL} & \text{Given} \\\hline 2.\; \angle KMJ \text{ and } \angle KML \text{ are right angles} & \; \\\hline 3.\; \angle KMJ \cong \angle KML & \text{All right angles are congruent} \\\hline 4.\; \overline{JK} \cong \overline{LK} & \; \\\hline 5.\; \overline{KM} \cong \overline{KM} & \; \\\hline 6.\; \triangle JKM \cong \triangle LKM & \text{HL} \\\hline\end{array} P Q R S \egin{aligned}&\textbf{Given: } \overline{PQ} \parallel \overline{RS} \\ &\qquad\quad\; \overline{PQ} \cong \overline{RS} \\&\textbf{Prove: } \triangle PQR \cong \triangle RSP\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{PQ} \parallel \overline{RS} & \; \\\hline 2.\; \angle QPR \cong \angle SRP & \; \\\hline 3.\; \overline{PQ} \cong \overline{RS} & \; \\\hline 4.\; \overline{PR} \cong \overline{PR} & \; \\\hline 5.\; \triangle PQR \cong \triangle RSP & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Alternate interior angles of parallel lines are congruent} \;\cdot\; \text{AA similarity} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Given} \;\cdot\; \text{Definition of midpoint} \;\cdot\; \text{HL} \;\cdot\; \text{SAS} \;\cdot\; \text{Base angles of an isosceles triangle are congruent} J K L M \egin{aligned}&\textbf{Given: } \overline{JK} \parallel \overline{LM} \\ &\qquad\quad\; \overline{JK} \cong \overline{LM} \\&\textbf{Prove: } \triangle JKL \cong \triangle LMJ\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{JK} \parallel \overline{LM} & \text{Given} \\\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 & \text{SAS} \\\hline\end{array} F G H I J \egin{aligned}&\textbf{Given: } \overline{FJ} \cong \overline{IJ} \\ &\qquad\quad\; \angle F \cong \angle I \\&\textbf{Prove: } \triangle FGJ \cong \triangle IHJ\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{FJ} \cong \overline{IJ} & \; \\\hline 2.\; \angle F \cong \angle I & \; \\\hline 3.\; \angle FJG \cong \angle IJH & \; \\\hline 4.\; \triangle FGJ \cong \triangle IHJ & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Given} \;\cdot\; \text{If base angles are congruent, the triangle is isosceles} \;\cdot\; \text{CPCTC} \;\cdot\; \text{Definition of a segment bisector} \;\cdot\; \text{If alternate exterior angles are congruent, the lines are parallel} \;\cdot\; \text{Vertical angles are congruent} \;\cdot\; \text{ASA} R S T U \egin{aligned}&\textbf{Given: } \overline{RS} \cong \overline{TS} \\ &\qquad\quad\; \overline{SU} \perp \overline{RT} \\&\textbf{Prove: } \triangle RSU \cong \triangle TSU\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{SU} \perp \overline{RT} & \text{Given} \\\hline 2.\; \angle SUR \text{ and } \angle SUT \text{ are right angles} & \; \\\hline 3.\; \angle SUR \cong \angle SUT & \; \\\hline 4.\; \overline{RS} \cong \overline{TS} & \text{Given} \\\hline 5.\; \overline{SU} \cong \overline{SU} & \text{Reflexive property} \\\hline 6.\; \triangle RSU \cong \triangle TSU & \; \\\hline\end{array} W X Y Z \egin{aligned}&\textbf{Given: } \overline{WX} \cong \overline{YX} \\ &\qquad\quad\; \overline{XZ} \perp \overline{WY} \\&\textbf{Prove: } \triangle WXZ \cong \triangle YXZ\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{XZ} \perp \overline{WY} & \; \\\hline 2.\; \angle XZW \text{ and } \angle XZY \text{ are right angles} & \; \\\hline 3.\; \angle XZW \cong \angle XZY & \; \\\hline 4.\; \overline{WX} \cong \overline{YX} & \; \\\hline 5.\; \overline{XZ} \cong \overline{XZ} & \; \\\hline 6.\; \triangle WXZ \cong \triangle YXZ & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{All right angles are congruent} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{HL} \;\cdot\; \text{Same-side interior angles of parallel lines are supplementary} \;\cdot\; \text{Angle addition postulate} \;\cdot\; \text{Given} \;\cdot\; \text{CPCTC} \;\cdot\; \text{Definition of perpendicular} \;\cdot\; \text{AAS}
Sigma Prep · sigmaprep.io/worksheets
Name
Proving Triangles CongruentAnswer keyVersion 1 Date
Complete each proof.
A B C D \egin{aligned}&\textbf{Given: } \overline{AC} bisects \angle BCD \\ &\qquad\quad\; \overline{BC} \cong \overline{DC} \\&\textbf{Prove: } \triangle ABC \cong \triangle ADC\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{AC} \text{ bisects } \angle BCD & \text{Given} \\\hline 2.\; \angle BCA \cong \angle DCA & \text{Definition of an angle bisector} \\\hline 3.\; \overline{BC} \cong \overline{DC} & \; \\\hline 4.\; \overline{AC} \cong \overline{AC} & \; \\\hline 5.\; \triangle ABC \cong \triangle ADC & \; \\\hline\end{array} 3. Given 4. Reflexive property 5. SAS 3. Given 4. Reflexive property 5. SAS R S T U \egin{aligned}&\textbf{Given: } \overline{RT} bisects \angle STU \\ &\qquad\quad\; \overline{ST} \cong \overline{UT} \\&\textbf{Prove: } \triangle RST \cong \triangle RUT\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{RT} \text{ bisects } \angle STU & \; \\\hline 2.\; \angle STR \cong \angle UTR & \; \\\hline 3.\; \overline{ST} \cong \overline{UT} & \; \\\hline 4.\; \overline{RT} \cong \overline{RT} & \; \\\hline 5.\; \triangle RST \cong \triangle RUT & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{SAS} \;\cdot\; \text{Supplements of congruent angles are congruent} \;\cdot\; \text{Linear pairs are supplementary} \;\cdot\; \text{If base angles are congruent, the triangle is isosceles} \;\cdot\; \text{Given} \;\cdot\; \text{Base angles of an isosceles triangle are congruent} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Definition of an angle bisector} 1. Given 2. Definition of an angle bisector 3. Given 4. Reflexive property 5. SAS 1. Given 2. Definition of an angle bisector 3. Given 4. Reflexive property 5. SAS J K L M \egin{aligned}&\textbf{Given: } \overline{JK} \cong \overline{LK} \\ &\qquad\quad\; \overline{KM} \perp \overline{JL} \\&\textbf{Prove: } \triangle JKM \cong \triangle LKM\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{KM} \perp \overline{JL} & \text{Given} \\\hline 2.\; \angle KMJ \text{ and } \angle KML \text{ are right angles} & \; \\\hline 3.\; \angle KMJ \cong \angle KML & \text{All right angles are congruent} \\\hline 4.\; \overline{JK} \cong \overline{LK} & \; \\\hline 5.\; \overline{KM} \cong \overline{KM} & \; \\\hline 6.\; \triangle JKM \cong \triangle LKM & \text{HL} \\\hline\end{array} 2. Definition of perpendicular 4. Given 5. Reflexive property 2. Definition of perpendicular 4. Given 5. Reflexive property P Q R S \egin{aligned}&\textbf{Given: } \overline{PQ} \parallel \overline{RS} \\ &\qquad\quad\; \overline{PQ} \cong \overline{RS} \\&\textbf{Prove: } \triangle PQR \cong \triangle RSP\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{PQ} \parallel \overline{RS} & \; \\\hline 2.\; \angle QPR \cong \angle SRP & \; \\\hline 3.\; \overline{PQ} \cong \overline{RS} & \; \\\hline 4.\; \overline{PR} \cong \overline{PR} & \; \\\hline 5.\; \triangle PQR \cong \triangle RSP & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Alternate interior angles of parallel lines are congruent} \;\cdot\; \text{AA similarity} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{Given} \;\cdot\; \text{Definition of midpoint} \;\cdot\; \text{HL} \;\cdot\; \text{SAS} \;\cdot\; \text{Base angles of an isosceles triangle are congruent} 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS 1. Given 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 5. SAS J K L M \egin{aligned}&\textbf{Given: } \overline{JK} \parallel \overline{LM} \\ &\qquad\quad\; \overline{JK} \cong \overline{LM} \\&\textbf{Prove: } \triangle JKL \cong \triangle LMJ\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{JK} \parallel \overline{LM} & \text{Given} \\\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 & \text{SAS} \\\hline\end{array} 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property 2. Alternate interior angles of parallel lines are congruent 3. Given 4. Reflexive property F G H I J \egin{aligned}&\textbf{Given: } \overline{FJ} \cong \overline{IJ} \\ &\qquad\quad\; \angle F \cong \angle I \\&\textbf{Prove: } \triangle FGJ \cong \triangle IHJ\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{FJ} \cong \overline{IJ} & \; \\\hline 2.\; \angle F \cong \angle I & \; \\\hline 3.\; \angle FJG \cong \angle IJH & \; \\\hline 4.\; \triangle FGJ \cong \triangle IHJ & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Given} \;\cdot\; \text{If base angles are congruent, the triangle is isosceles} \;\cdot\; \text{CPCTC} \;\cdot\; \text{Definition of a segment bisector} \;\cdot\; \text{If alternate exterior angles are congruent, the lines are parallel} \;\cdot\; \text{Vertical angles are congruent} \;\cdot\; \text{ASA} 1. Given 2. Given 3. Vertical angles are congruent 4. ASA 1. Given 2. Given 3. Vertical angles are congruent 4. ASA R S T U \egin{aligned}&\textbf{Given: } \overline{RS} \cong \overline{TS} \\ &\qquad\quad\; \overline{SU} \perp \overline{RT} \\&\textbf{Prove: } \triangle RSU \cong \triangle TSU\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{SU} \perp \overline{RT} & \text{Given} \\\hline 2.\; \angle SUR \text{ and } \angle SUT \text{ are right angles} & \; \\\hline 3.\; \angle SUR \cong \angle SUT & \; \\\hline 4.\; \overline{RS} \cong \overline{TS} & \text{Given} \\\hline 5.\; \overline{SU} \cong \overline{SU} & \text{Reflexive property} \\\hline 6.\; \triangle RSU \cong \triangle TSU & \; \\\hline\end{array} 2. Definition of perpendicular 3. All right angles are congruent 6. HL 2. Definition of perpendicular 3. All right angles are congruent 6. HL W X Y Z \egin{aligned}&\textbf{Given: } \overline{WX} \cong \overline{YX} \\ &\qquad\quad\; \overline{XZ} \perp \overline{WY} \\&\textbf{Prove: } \triangle WXZ \cong \triangle YXZ\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{XZ} \perp \overline{WY} & \; \\\hline 2.\; \angle XZW \text{ and } \angle XZY \text{ are right angles} & \; \\\hline 3.\; \angle XZW \cong \angle XZY & \; \\\hline 4.\; \overline{WX} \cong \overline{YX} & \; \\\hline 5.\; \overline{XZ} \cong \overline{XZ} & \; \\\hline 6.\; \triangle WXZ \cong \triangle YXZ & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{All right angles are congruent} \;\cdot\; \text{Reflexive property} \;\cdot\; \text{HL} \;\cdot\; \text{Same-side interior angles of parallel lines are supplementary} \;\cdot\; \text{Angle addition postulate} \;\cdot\; \text{Given} \;\cdot\; \text{CPCTC} \;\cdot\; \text{Definition of perpendicular} \;\cdot\; \text{AAS} 1. Given 2. Definition of perpendicular 3. All right angles are congruent 4. Given 5. Reflexive property 6. HL 1. Given 2. Definition of perpendicular 3. All right angles are congruent 4. Given 5. Reflexive property 6. HL
Found a mistake on this sheet?
How to do these Given a shared side, which postulate finishes the proof?
Two pairs of sides are marked congruent. The third pair is the shared side, congruent to itself by the reflexive property. Three pairs of sides. The answer is SSS
Where students go wrong Marking a pattern that does not prove anything. Two sides and an angle that is not between them is SSA, and SSA proves nothing at all.
Also called triangle congruence proofs, two column proofs triangles, SSS SAS ASA AAS proofs or congruent triangle proofs.
What you can put on this worksheet
Fill in the missing reasons \egin{aligned}&\textbf{Given: } \overline{WX} \cong \overline{YZ} \\ &\qquad\quad\; \overline{XY} \cong \overline{ZW} \\&\textbf{Prove: } \triangle WXY \cong \triangle YZW\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} \cong \overline{YZ} & \text{Given} \\\hline 2.\; \overline{XY} \cong \overline{ZW} & \; \\\hline 3.\; \overline{WY} \cong \overline{WY} & \text{Reflexive property} \\\hline 4.\; \triangle WXY \cong \triangle YZW & \; \\\hline\end{array} → 2. Given 4. SSS 2. Given 4. SSS
Fill in every reason \egin{aligned}&\textbf{Given: } \overline{WX} \cong \overline{YZ} \\ &\qquad\quad\; \overline{XY} \cong \overline{ZW} \\&\textbf{Prove: } \triangle WXY \cong \triangle YZW\end{aligned} \\[4pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{WX} \cong \overline{YZ} & \; \\\hline 2.\; \overline{XY} \cong \overline{ZW} & \; \\\hline 3.\; \overline{WY} \cong \overline{WY} & \; \\\hline 4.\; \triangle WXY \cong \triangle YZW & \; \\\hline\end{array} \\[3pt] \text{Word bank: } \small \text{Given} \;\cdot\; \text{SSS} \;\cdot\; \text{Addition property} \;\cdot\; \text{All radii of a circle are congruent} \;\cdot\; \text{Corresponding angles of parallel lines are congruent} \;\cdot\; \text{Complements of congruent angles are congruent} \;\cdot\; \text{Reflexive property} → 1. Given 2. Given 3. Reflexive property 4. SSS 1. Given 2. Given 3. Reflexive property 4. SSS
Fill in the missing statements \egin{aligned}&\textbf{Given: } \overline{WX} \cong \overline{YZ} \\ &\qquad\quad\; \overline{XY} \cong \overline{ZW} \\&\textbf{Prove: } \triangle WXY \cong \triangle YZW\end{aligned} \\[4pt] \text{Give the missing statements.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \overline{WX} \cong \overline{YZ} & \text{Given} \\\hline 2.\; \; & \text{Given} \\\hline 3.\; \overline{WY} \cong \overline{WY} & \text{Reflexive property} \\\hline 4.\; \; & \text{SSS} \\\hline\end{array} → 2. X Y ‾ ≅ Z W ‾ 4. △ W X Y ≅ △ Y Z W 2. X Y ≅ Z W 4. △ W X Y ≅ △ Y Z W
Write the whole proof \egin{aligned}&\textbf{Given: } \overline{WX} \cong \overline{YZ} \\ &\qquad\quad\; \overline{XY} \cong \overline{ZW} \\&\textbf{Prove: } \triangle WXY \cong \triangle YZW\end{aligned} \\[4pt] \text{Write the proof. It takes 4 lines.} \\[2pt] \small\def\arraystretch{1.7}\egin{array}{|l|l|}\hline\ extbf{Statements} & \ extbf{Reasons} \\\hline1.\; \; & \; \\\hline 2.\; \; & \; \\\hline 3.\; \; & \; \\\hline 4.\; \; & \; \\\hline\end{array} → 1. W X ‾ ≅ Y Z ‾ Given 2. X Y ‾ ≅ Z W ‾ Given 3. W Y ‾ ≅ W Y ‾ Reflexive property 4. △ W X Y ≅ △ Y Z W SSS 1. W X ≅ Y Z Given 2. X Y ≅ Z W Given 3. WY ≅ WY Reflexive property 4. △ W X Y ≅ △ Y Z W SSS
Name the postulate that finishes the proof \egin{aligned}&\textbf{Given: } \overline{WX} \cong \overline{YZ} \\ &\qquad\quad\; \overline{XY} \cong \overline{ZW} \\&\textbf{Prove: } \triangle WXY \cong \triangle YZW\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.\; \overline{WX} \cong \overline{YZ} & \text{Given} \\\hline 2.\; \overline{XY} \cong \overline{ZW} & \text{Given} \\\hline 3.\; \overline{WY} \cong \overline{WY} & \text{Reflexive property} \\\hline 4.\; \triangle WXY \cong \triangle YZW & \; \\\hline\end{array} → SSS Questions about these worksheets Are these proving triangles congruent worksheets free? + Yes. Every proving triangles congruent 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 proving triangles congruent 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 proving triangles congruent 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 proving triangles congruent 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 proving triangles congruent 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 proving triangles congruent? + 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 proving triangles congruent 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 proving triangles congruent 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 proving triangles congruent 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 proving triangles congruent? + Marking a pattern that does not prove anything. Two sides and an angle that is not between them is SSA, and SSA proves nothing at all.
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