The task involves determining which postulate or theorem can be used to conclude that the triangles in each pair are congruent. Here is a detailed explanation of the solution for each pair of triangles:
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1.
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Triangles: ΔFGH and ΔIHG
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Given:
- ∠F ≅ ∠I (marked)
- GH ≅ HG (reflexive side)
- ∠G ≅ ∠H (marked)
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Postulate/Theorem: SAS (Side-Angle-Side)
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Reasoning: The two sides and the included angle between them are congruent.
---
2.
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Triangles: ΔNOP and ΔQRP
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Given:
- NO ≅ QR
- OP ≅ RP
- NP ≅ PQ
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Postulate/Theorem: SSS (Side-Side-Side)
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Reasoning: All three sides of one triangle are congruent to the corresponding sides of the other triangle.
---
3.
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Triangles: ΔABC and ΔDEC
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Given:
- ∠A ≅ ∠D
- AC ≅ DE
- ∠C ≅ ∠E
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Postulate/Theorem: ASA (Angle-Side-Angle)
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Reasoning: Two angles and the included side between them are congruent.
---
4.
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Triangles: ΔRST and ΔUTS
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Given:
- ∠R ≅ ∠U
- ST ≅ TS (reflexive side)
- ∠S ≅ ∠T
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Postulate/Theorem: ASA (Angle-Side-Angle)
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Reasoning: Two angles and the included side between them are congruent.
---
5.
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Triangles: ΔJKL and ΔMLK
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Given:
- ∠J ≅ ∠M
- ∠K ≅ ∠L
- JL ≅ KL
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Postulate/Theorem: AAS (Angle-Angle-Side)
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Reasoning: Two angles and a non-included side are congruent.
---
6.
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Triangles: ΔNQP and ΔPQN
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Given:
- NQ ≅ PQ
- QP ≅ QP (reflexive side)
- ∠N ≅ ∠P
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Postulate/Theorem: SAS (Side-Angle-Side)
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Reasoning: Two sides and the included angle between them are congruent.
---
7.
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Triangles: ΔABE and ΔCDE
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Given:
- ∠A ≅ ∠C
- BE ≅ DE
- ∠B ≅ ∠D
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Postulate/Theorem: AAS (Angle-Angle-Side)
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Reasoning: Two angles and a non-included side are congruent.
---
8.
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Triangles: ΔFGH and ΔGHF
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Given:
- ∠F ≅ ∠G
- FH ≅ GH
- ∠H ≅ ∠H (reflexive angle)
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Postulate/Theorem: ASA (Angle-Side-Angle)
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Reasoning: Two angles and the included side between them are congruent.
---
9.
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Triangles: ΔJKL and ΔLMN
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Given:
- JK ≅ LM
- KL ≅ MN
- JL ≅ LN
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Postulate/Theorem: SSS (Side-Side-Side)
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Reasoning: All three sides of one triangle are congruent to the corresponding sides of the other triangle.
---
10.
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Triangles: ΔNOQ and ΔPOQ
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Given:
- ∠N ≅ ∠P
- OQ ≅ OQ (reflexive side)
- ∠O ≅ ∠O
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Postulate/Theorem: ASA (Angle-Side-Angle)
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Reasoning: Two angles and the included side between them are congruent.
---
11.
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Triangles: ΔJKL and ΔMLK
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Given:
- ∠J ≅ ∠M
- JK ≅ ML
- ∠K ≅ ∠L
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Postulate/Theorem: Not Congruent
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Reasoning: Although two angles and a side are marked, the side is not the included side between the two angles, so neither ASA nor AAS applies.
---
12.
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Triangles: ΔRST and ΔTUW
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Given:
- RS ≅ TU
- ST ≅ UW
- RT ≅ TW
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Postulate/Theorem: SSS (Side-Side-Side)
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Reasoning: All three sides of one triangle are congruent to the corresponding sides of the other triangle.
---
Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & \text{SAS} \\
2. & \text{SSS} \\
3. & \text{ASA} \\
4. & \text{ASA} \\
5. & \text{AAS} \\
6. & \text{SAS} \\
7. & \text{AAS} \\
8. & \text{ASA} \\
9. & \text{SSS} \\
10. & \text{ASA} \\
11. & \text{Not Congruent} \\
12. & \text{SSS} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of geometry triangle congruence worksheet answers.
![FREE Printable Triangle Congruence Worksheets [PDFs] Brighterly](/images2/geometry-triangle-congruence-worksheet-answers/geometry-triangle-congruence-worksheet-answers-30.jpg)
