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Triangle CAT is transformed by a sequence of rigid motions that maps onto triangle DOG. Which three congruency statements would show ASA congruency for these triangles? (select all that apply)

A.∠ A ≅ ∠ T

B.CA ≅ DO

C.AT ≅ OG

D.CT ≅ DG

E.∠ A ≅ ∠ O

F.∠ C ≅ ∠ D



Answer :

mhanifa

Answer:

  • B, E and F.

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Since the triangles CAT and DOG overlap, their corresponding parts are congruent.

As we are looking for ASA congruency, we need to select two angles and the included side.

Let's review the given options, considering names of triangles and the order of vertices in those names.

A. ∠ A ≅ ∠ T  

  • Incorrect as angles T and A are not corresponding.

B. CA ≅ DO

  • Yes, possible side.

C. AT ≅ OG

  • Yes, possible side.

D. CT ≅ DG

  • Yes, possible side.

E. ∠ A ≅ ∠ O

  • Yes, possible angle.

F. ∠ C ≅ ∠ D

  • Yes, possible angle.

So we have corresponding angles A and C and the included side must be AC.

Looking, at the options, we can get ASA with combination of options B, E and F.

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