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Given: AB¯≅AC¯;BN¯⊥AC¯;CM¯⊥AB¯ .

Explain how you could prove that ΔABN≅ΔACM.

Short Answer

Expert verified

In the triangles ΔABNand ΔACM, it can be noticed that:

AB=AC(given)∠A=∠A(reflexiveproperty)∠ANB=∠AMC=90°

Therefore, the triangles ΔABNand ΔACMare the congruent triangles by usingAAS postulate.

Therefore, ΔABN≅ΔACMcan be proved by AASpostulate.

Step by step solution

01

- Observe the given diagram.

The given diagram is:

02

- Description of step.

In the triangles ΔABNand ΔACM, it can be noticed that:

AB=AC(given)∠A=∠A(reflexiveproperty)∠ANB=∠AMC=90°

Therefore, the trianglesΔABN andΔACM are the congruent triangles by usingAAS postulate.

03

- Description of step.

Therefore, the trianglesΔABN andΔACM are the congruent triangles by usingAAS postulate.

Therefore, ΔABN≅ΔACMcan be proved by AASpostulate.

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