In Exercises 9-14, decide whether enough information

Mathematics

1 answer:

Degger [83]2 years ago

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The triangles that can be proved to be congruent by the SAS Congruence Theorem are:

10. ΔLMN and ΔNQP

13. ΔEFH and ΔGHF

The triangles that cannot be proved to be congruent by the SAS Congruence Theorem due to insufficient information are:

9. ΔABD and ΔCDB

12. ΔQRV and ΔTSU

14. ΔKLM and ΔMNK

11. ΔYXZ and ΔWXZ

<h3>What is the SAS Congruence Theorem?</h3>

If two triangles have two pairs of corresponding sides that are congruent, and a pair of corresponding included angle that are congruent, both triangles can be proven to be congruent triangles by the SAS Congruence Theorem.

Thus:

9. ΔABD and ΔCDB have:

one pair of congruent non-included angles - ∠ABD ≅ ∠CDB
two pairs of congruent sides - AD ≅ BC, and BD ≅ BD

ΔABD and ΔCDB lack a pair of included angles, therefore, the information given is not enough to prove the triangles are congruent by the SAS Congruence Theorem.

10. ΔLMN and ΔNQP have:

one pair of congruent included angles - ∠LMN ≅ ∠NQP
two pairs of congruent sides - LM ≅ NQ, and MN ≅ QP

ΔLMN and ΔNQP, therefore, have enough information to prove that they are congruent triangles by the SAS Congruence Theorem.

11. ΔYXZ and ΔWXZ have:

one pair of congruent non-included angles - ∠YXZ ≅ ∠WXZ
two pairs of congruent sides - XZ ≅ XZ, and XW ≅ YZ

ΔYXZ and ΔWXZ lack a pair of included angles, therefore, the information given is not enough to prove the triangles are congruent by the SAS Congruence Theorem.

12. ΔQRV and ΔTSU do not have enough information to prove they are congruent by the SAS Congruence Theorem.

13. ΔEFH and ΔGHF have two pairs of congruent sides and a pair of congruent included angles, therefore, there is enough information to prove they are congruent by the SAS Congruence Theorem.

14. ΔKLM and ΔMNK do not have enough information to prove they are congruent by the SAS Congruence Theorem.

Therefore, the triangles that can be proved to be congruent by the SAS Congruence Theorem are: