Respuesta :
By definition, congruent triangles should have all the corresponding sides and all the corresponding angles equal or congruent to each other. Thus, in the given question, all corresponding sides and angles of ΔEFG and ΔE'F'G' should be congruent. But, as we can see clearly it is given that, EF = 10 and E'F'= 12, thus, the corresponding sides EF and E'F' are not equal. Thus, we can never prove that:
[tex] \Delta EFG\cong\Delta E'F'G' [/tex]
Thus, [tex] \Delta EFG\ncong\Delta E'F'G' [/tex]
For the AAS theorem, when two angle and one side of the triangle, equal to the two angles and same side of the other for congruent triangle . There is A, B and option C can be used to prove the triangle congurent with SAS rule but not with AAS rule.
What is triangle congruence theorem?
Two triangle are congruent when the shape and size of both the triangle are same.
Triangle congruence theorem are-
- Angle-Side-Angle theorem (AAS)- This theorem states that two triangle is congruent when two angle and one side of the triangle are respectively equal to the two angles and same side of the other triangle.
- Side-Side-Side theorem (SSS)- When the three sides of the one triangle is equal to the three sides of the other triangle respectively, then the triangle are congruent.
- Side-Angle-Side theorem (SAS)- Two sides and the included angle of are equal to the two sides and one angle of other triangle respectively.
Given information-
In the given ΔEFG and ΔE'F'G' should be congruent by the AAS as,
[tex]\Delta EFG=\Delta E'F'G'[/tex]
For the AAS, two triangle is congruent when two angle and one side of the triangle are respectively equal to the two angles and same side of the other triangle.
Therefore the two sides and one angle must be equal to prove two triangle congruent.
In the given options two sides given equal which are,
[tex]EG=E'G'=12\\FG=F'G'=15[/tex]
One angle is equal in the given options which is,
[tex]m\angle G=m\angle G=42^o[/tex]
Here two sides and one angle is equal instead of two angles and one side from the given option. Thus the two triangle ΔEFG and ΔE'F'G' are congurent by SAS rule and not by the AAS rule.
Learn more about the triangle congruence theorem here;
https://brainly.com/question/19258025
