Here is the solution for each pair of triangles on the worksheet, identifying the correct congruence postulate or theorem (SSS, SAS, ASA, AAS, or HL).
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1. Triangles FGI and HGI
- Given: FG ≅ HG (marked with one tick), GI is common to both triangles, ∠FGI ≅ ∠HGI (marked with arcs).
- We have two sides and the included angle equal.
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Answer: SAS (Side-Angle-Side)
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2. Triangles NOP and NQP
- Given: NO ≅ QP (two ticks), OP ≅ NQ (one tick), NP is common to both triangles.
- All three sides are equal.
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Answer: SSS (Side-Side-Side)
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3. Triangles ABC and EDC
- Given: ∠B ≅ ∠D (marked with arcs), BC ≅ DC (marked with ticks), ∠ACB ≅ ∠ECD (vertical angles — always congruent).
- Two angles and the included side are equal.
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Answer: ASA (Angle-Side-Angle)
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4. Triangles RSU and TSU
- Given: ∠RSU ≅ ∠TSU (arcs), ∠RUS ≅ ∠TUS (arcs), SU is common to both triangles.
- Two angles and the included side are equal.
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Answer: ASA (Angle-Side-Angle)
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5. Triangles JKM and LKM
- Given: ∠J ≅ ∠L (arcs), ∠JKM ≅ ∠LKM (arcs), KM is common to both triangles.
- Two angles and a non-included side (KM) are equal.
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Answer: AAS (Angle-Angle-Side)
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6. Triangles NOP and QOP
- Given: NO ≅ QO (one tick), NP ≅ QP (two ticks), OP is common to both triangles.
- All three sides are equal.
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Answer: SSS (Side-Side-Side)
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7. Triangles ABC and EDC
- Given: AB ≅ DE (one tick), ∠A ≅ ∠D (arcs), ∠ACB ≅ ∠ECD (vertical angles).
- Two angles and a non-included side are equal.
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Answer: AAS (Angle-Angle-Side)
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8. Triangles FGI and HGI
- Given: ∠F ≅ ∠H (arcs), ∠FGI ≅ ∠HGI (arcs), GI is common to both triangles.
- Two angles and the included side are equal.
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Answer: ASA (Angle-Side-Angle)
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9. Triangles JKM and LKM
- Given: JK ≅ LM (one tick), JM ≅ KL (two ticks), KM is common to both triangles.
- All three sides are equal.
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Answer: SSS (Side-Side-Side)
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10. Triangles NOP and QOP
- Given: ∠N ≅ ∠Q (arcs), ∠OPN ≅ ∠OPQ (arcs), OP is common to both triangles.
- Two angles and the included side are equal.
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Answer: ASA (Angle-Side-Angle)
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11. Triangles JKM and LKM
- Given: JK ≅ LM (one tick), JM ≅ KL (two ticks), KM is common to both triangles.
- All three sides are equal.
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Answer: SSS (Side-Side-Side)
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12. Triangles RSU and TSU
- Given: RS ≅ TU (one tick), ST ≅ RU (two ticks), SU is common to both triangles.
- All three sides are equal.
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Answer: SSS (Side-Side-Side)
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✔ Final Answers Summary:
1. SAS
2. SSS
3. ASA
4. ASA
5. AAS
6. SSS
7. AAS
8. ASA
9. SSS
10. ASA
11. SSS
12. SSS
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Parent Tip: Review the logic above to help your child master the concept of geometry triangle congruence worksheet answers.
