Below are \triangle ABC△ABCtriangle, A, B, C and \triangle DEF△DEFtriangle, D, E, F. We assume that AB=DEAB=DEA, B, equals, D, E, AC=DFAC=DFA, C, equals, D, F, and m\angle A=m\angle Dm∠A=m∠Dm, angle, A, equals, m, angle, D. Here is a rough outline of a proof that \triangle ABC\cong\triangle DEF△ABC≅△DEFtriangle, A, B, C, \cong, triangle, D, E, F:
We can map \triangle ABC△ABCtriangle, A, B, C using a sequence of rigid transformations so that A'=DA
′
=DA, prime, equals, D, B'B
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B, prime and EEE are on the same ray from DDD, and C'C
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C, prime and FFF are on the same ray from DDD. [Show drawing.]
As a result of these transformations, B'B
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B, prime must coincide with EEE. [Show drawing.]
As a result of these transformations, C'C
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C, prime must coincide with FFF. [Show drawing.]
Answer two questions about this proof.
1) How did we show that the triangles were congruent?
Choose 1
Choose 1

(Choice A)
A
We mapped one figure onto the other using rigid transformations.

(Choice B)
B
We mapped one figure onto the other using any kind of transformations.

(Choice C)
C
We showed that all corresponding sides had equal lengths and all corresponding angles had equal measures.
2) What triangles did we show are congruent?
Choose 1
Choose 1

(Choice A)
A
Triangles where 222 pairs of corresponding sides have the same length, and the included corresponding angles have the same measure

(Choice B)
B
Triangles where 111 pair of corresponding sides have the same length, and 111 pair of corresponding angles have the same measure

(Choice C)
C
All triangles