Geometry Files: Triangle Congruence - Insert Clever Math Pun Here - Free Printable
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Step-by-step solution for: Geometry Files: Triangle Congruence - Insert Clever Math Pun Here
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Show Answer Key & Explanations
Step-by-step solution for: Geometry Files: Triangle Congruence - Insert Clever Math Pun Here
1) Given: $\overline{AB} \parallel \overline{CD}$; $\overline{AB} \cong \overline{CD}$
Prove: $\triangle ABC \cong \triangle DCB$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{AB} \parallel \overline{CD}$ | Given |
| 2. $\angle ABC \cong \angle DCB$ | Alternate Interior Angles Theorem |
| 3. $\overline{AB} \cong \overline{CD}$ | Given |
| 4. $\overline{BC} \cong \overline{CB}$ | Reflexive Property of Congruence |
| 5. $\triangle ABC \cong \triangle DCB$ | SAS Congruence Postulate |
2) Given: $\angle J \cong \angle M$, K is midpoint of $\overline{JM}$
Prove: $\triangle JKN \cong \triangle MKL$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle J \cong \angle M$ | Given |
| 2. K is midpoint of $\overline{JM}$ | Given |
| 3. $\overline{JK} \cong \overline{MK}$ | Definition of Midpoint |
| 4. $\angle JKN \cong \angle MKL$ | Vertical Angles Theorem |
| 5. $\triangle JKN \cong \triangle MKL$ | ASA Congruence Postulate |
3) Given: $\angle X \cong \angle W$, $\overline{ZT} \perp \overline{XW}$
Prove: $\triangle XTZ \cong \triangle WTZ$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle X \cong \angle W$ | Given |
| 2. $\overline{ZT} \perp \overline{XW}$ | Given |
| 3. $\angle ZTX \cong \angle ZTW$ | Definition of Perpendicular Lines (both are right angles) |
| 4. $\overline{ZT} \cong \overline{ZT}$ | Reflexive Property of Congruence |
| 5. $\triangle XTZ \cong \triangle WTZ$ | AAS Congruence Theorem |
4) Given: $\overline{RM} \perp \overline{LP}$; $\overline{RL} \cong \overline{RP}$
Prove: $\triangle RML \cong \triangle RMP$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{RM} \perp \overline{LP}$ | Given |
| 2. $\angle RML \cong \angle RMP$ | Definition of Perpendicular Lines (both are right angles) |
| 3. $\overline{RL} \cong \overline{RP}$ | Given |
| 4. $\overline{RM} \cong \overline{RM}$ | Reflexive Property of Congruence |
| 5. $\triangle RML \cong \triangle RMP$ | HL Congruence Theorem (for right triangles) |
5) Given: $\overline{AC}$ bisects $\angle BCD$; $\overline{BC} \cong \overline{DC}$
Prove: $\triangle ABC \cong \triangle ADC$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{AC}$ bisects $\angle BCD$ | Given |
| 2. $\angle BCA \cong \angle DCA$ | Definition of Angle Bisector |
| 3. $\overline{BC} \cong \overline{DC}$ | Given |
| 4. $\overline{AC} \cong \overline{AC}$ | Reflexive Property of Congruence |
| 5. $\triangle ABC \cong \triangle ADC$ | SAS Congruence Postulate |
6) Given: $\overline{AB} \cong \overline{DC}$; $\overline{AD} \cong \overline{BC}$
Prove: $\triangle ABD \cong \triangle CDB$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{AB} \cong \overline{DC}$ | Given |
| 2. $\overline{AD} \cong \overline{BC}$ | Given |
| 3. $\overline{BD} \cong \overline{DB}$ | Reflexive Property of Congruence |
| 4. $\triangle ABD \cong \triangle CDB$ | SSS Congruence Postulate |
7) Given: $\angle R \cong \angle U$; $\overline{ST}$ bisects $\angle RSU$
Prove: $\triangle RST \cong \triangle UST$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle R \cong \angle U$ | Given |
| 2. $\overline{ST}$ bisects $\angle RSU$ | Given |
| 3. $\angle RST \cong \angle UST$ | Definition of Angle Bisector |
| 4. $\overline{ST} \cong \overline{ST}$ | Reflexive Property of Congruence |
| 5. $\triangle RST \cong \triangle UST$ | AAS Congruence Theorem |
8) Given: $\angle BDA$ and $\angle BDC$ are right angles; $\overline{BA} \cong \overline{BC}$
Prove: $\triangle BDA \cong \triangle BDC$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle BDA$ and $\angle BDC$ are right angles | Given |
| 2. $\angle BDA \cong \angle BDC$ | All right angles are congruent |
| 3. $\overline{BA} \cong \overline{BC}$ | Given |
| 4. $\overline{BD} \cong \overline{BD}$ | Reflexive Property of Congruence |
| 5. $\triangle BDA \cong \triangle BDC$ | HL Congruence Theorem (for right triangles) |
9) Given: $\overline{RN} \perp \overline{MP}$; N is midpoint of $\overline{MP}$
Prove: $\triangle RNM \cong \triangle RNP$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{RN} \perp \overline{MP}$ | Given |
| 2. $\angle RNM \cong \angle RNP$ | Definition of Perpendicular Lines (both are right angles) |
| 3. N is midpoint of $\overline{MP}$ | Given |
| 4. $\overline{MN} \cong \overline{PN}$ | Definition of Midpoint |
| 5. $\overline{RN} \cong \overline{RN}$ | Reflexive Property of Congruence |
| 6. $\triangle RNM \cong \triangle RNP$ | SAS Congruence Postulate |
10) Given: $\angle C \cong \angle D$; $\overline{AB} \perp \overline{CD}$
Prove: $\triangle ABC \cong \triangle ABD$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle C \cong \angle D$ | Given |
| 2. $\overline{AB} \perp \overline{CD}$ | Given |
| 3. $\angle ABC \cong \angle ABD$ | Definition of Perpendicular Lines (both are right angles) |
| 4. $\overline{AB} \cong \overline{AB}$ | Reflexive Property of Congruence |
| 5. $\triangle ABC \cong \triangle ABD$ | AAS Congruence Theorem |
Prove: $\triangle ABC \cong \triangle DCB$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{AB} \parallel \overline{CD}$ | Given |
| 2. $\angle ABC \cong \angle DCB$ | Alternate Interior Angles Theorem |
| 3. $\overline{AB} \cong \overline{CD}$ | Given |
| 4. $\overline{BC} \cong \overline{CB}$ | Reflexive Property of Congruence |
| 5. $\triangle ABC \cong \triangle DCB$ | SAS Congruence Postulate |
2) Given: $\angle J \cong \angle M$, K is midpoint of $\overline{JM}$
Prove: $\triangle JKN \cong \triangle MKL$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle J \cong \angle M$ | Given |
| 2. K is midpoint of $\overline{JM}$ | Given |
| 3. $\overline{JK} \cong \overline{MK}$ | Definition of Midpoint |
| 4. $\angle JKN \cong \angle MKL$ | Vertical Angles Theorem |
| 5. $\triangle JKN \cong \triangle MKL$ | ASA Congruence Postulate |
3) Given: $\angle X \cong \angle W$, $\overline{ZT} \perp \overline{XW}$
Prove: $\triangle XTZ \cong \triangle WTZ$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle X \cong \angle W$ | Given |
| 2. $\overline{ZT} \perp \overline{XW}$ | Given |
| 3. $\angle ZTX \cong \angle ZTW$ | Definition of Perpendicular Lines (both are right angles) |
| 4. $\overline{ZT} \cong \overline{ZT}$ | Reflexive Property of Congruence |
| 5. $\triangle XTZ \cong \triangle WTZ$ | AAS Congruence Theorem |
4) Given: $\overline{RM} \perp \overline{LP}$; $\overline{RL} \cong \overline{RP}$
Prove: $\triangle RML \cong \triangle RMP$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{RM} \perp \overline{LP}$ | Given |
| 2. $\angle RML \cong \angle RMP$ | Definition of Perpendicular Lines (both are right angles) |
| 3. $\overline{RL} \cong \overline{RP}$ | Given |
| 4. $\overline{RM} \cong \overline{RM}$ | Reflexive Property of Congruence |
| 5. $\triangle RML \cong \triangle RMP$ | HL Congruence Theorem (for right triangles) |
5) Given: $\overline{AC}$ bisects $\angle BCD$; $\overline{BC} \cong \overline{DC}$
Prove: $\triangle ABC \cong \triangle ADC$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{AC}$ bisects $\angle BCD$ | Given |
| 2. $\angle BCA \cong \angle DCA$ | Definition of Angle Bisector |
| 3. $\overline{BC} \cong \overline{DC}$ | Given |
| 4. $\overline{AC} \cong \overline{AC}$ | Reflexive Property of Congruence |
| 5. $\triangle ABC \cong \triangle ADC$ | SAS Congruence Postulate |
6) Given: $\overline{AB} \cong \overline{DC}$; $\overline{AD} \cong \overline{BC}$
Prove: $\triangle ABD \cong \triangle CDB$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{AB} \cong \overline{DC}$ | Given |
| 2. $\overline{AD} \cong \overline{BC}$ | Given |
| 3. $\overline{BD} \cong \overline{DB}$ | Reflexive Property of Congruence |
| 4. $\triangle ABD \cong \triangle CDB$ | SSS Congruence Postulate |
7) Given: $\angle R \cong \angle U$; $\overline{ST}$ bisects $\angle RSU$
Prove: $\triangle RST \cong \triangle UST$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle R \cong \angle U$ | Given |
| 2. $\overline{ST}$ bisects $\angle RSU$ | Given |
| 3. $\angle RST \cong \angle UST$ | Definition of Angle Bisector |
| 4. $\overline{ST} \cong \overline{ST}$ | Reflexive Property of Congruence |
| 5. $\triangle RST \cong \triangle UST$ | AAS Congruence Theorem |
8) Given: $\angle BDA$ and $\angle BDC$ are right angles; $\overline{BA} \cong \overline{BC}$
Prove: $\triangle BDA \cong \triangle BDC$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle BDA$ and $\angle BDC$ are right angles | Given |
| 2. $\angle BDA \cong \angle BDC$ | All right angles are congruent |
| 3. $\overline{BA} \cong \overline{BC}$ | Given |
| 4. $\overline{BD} \cong \overline{BD}$ | Reflexive Property of Congruence |
| 5. $\triangle BDA \cong \triangle BDC$ | HL Congruence Theorem (for right triangles) |
9) Given: $\overline{RN} \perp \overline{MP}$; N is midpoint of $\overline{MP}$
Prove: $\triangle RNM \cong \triangle RNP$
| Statement | Reason |
| :--- | :--- |
| 1. $\overline{RN} \perp \overline{MP}$ | Given |
| 2. $\angle RNM \cong \angle RNP$ | Definition of Perpendicular Lines (both are right angles) |
| 3. N is midpoint of $\overline{MP}$ | Given |
| 4. $\overline{MN} \cong \overline{PN}$ | Definition of Midpoint |
| 5. $\overline{RN} \cong \overline{RN}$ | Reflexive Property of Congruence |
| 6. $\triangle RNM \cong \triangle RNP$ | SAS Congruence Postulate |
10) Given: $\angle C \cong \angle D$; $\overline{AB} \perp \overline{CD}$
Prove: $\triangle ABC \cong \triangle ABD$
| Statement | Reason |
| :--- | :--- |
| 1. $\angle C \cong \angle D$ | Given |
| 2. $\overline{AB} \perp \overline{CD}$ | Given |
| 3. $\angle ABC \cong \angle ABD$ | Definition of Perpendicular Lines (both are right angles) |
| 4. $\overline{AB} \cong \overline{AB}$ | Reflexive Property of Congruence |
| 5. $\triangle ABC \cong \triangle ABD$ | AAS Congruence Theorem |
Parent Tip: Review the logic above to help your child master the concept of geometry triangle congruence worksheet.
