Answer :
Answer:
The picture that does not contain enough information to prove that ΔABC = ΔDEF is
(3) Picture (3)
Step-by-step explanation:
The given information in picture (3) is the Angle-Side-Side of ΔABC corresponds with the Angle-Side-Side of ΔDEF,
However, the condition of Angle-Side-Side of ΔABC, is not sufficient to prove that ΔABC is congruent to ΔDEF congruency because the length of the unknown side can have two possible values
1. The set of triangles ABC and DEF that does not contain enough information to prove that both triangles are congruent by any Congruence Theorem is in: Figure 3
2. The Congruence Theorem that can be used to justify why triangles ABC and ADC are congruent is: SAS Congruence Theorem.
1. The set of triangles ABC and DEF in figure 1 shows that:
- Two angles and one included side in triangle ABC are congruent to two corresponding angles and one included side in triangle DEF.
Therefore, Triangles ABC and DEF are congruent by the ASA Congruence Theorem.
The set of triangles ABC and DEF in figure 2 shows that:
- Two sides and one included angle in triangle ABC are congruent to two corresponding sides and one included angle in triangle DEF.
Therefore, Triangles ABC and DEF are congruent by the SAS Congruence Theorem.
The set of triangles ABC and DEF in figure 2 shows that:
- there is no enough information to prove that triangles ABC is congruent to triangle DEF by any Congruence Theorem.
The set of triangles ABC and DEF in figure 2 shows that:
- Three sides in triangle ABC that are congruent to three corresponding sides in triangle DEF.
Therefore, Triangles ABC and DEF are congruent by the SSS Congruence Theorem.
Only the picture in figure 3 doesn't contain enough information to prove triangles ABC and DEF are congruent.
2. The two triangles ABC and CDA in the picture given shows that:
- Two sides and one included angle in triangle ABC are congruent to two corresponding sides and one included angle in triangle ADC.
Therefore, Triangles ABC and ADC can be proved to be congruent by the SAS Congruence Theorem.
In summary:
1. The set of triangles ABC and DEF that does not contain enough information to prove that both triangles are congruent by any Congruence Theorem is in: Figure 3
2. The Congruence Theorem that can be used to justify why triangles ABC and ADC are congruent is: SAS Congruence Theorem.
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