There are two triangles. For the first triangle, the vertices are A, B and C. m<A =65 degrees, m<B=70 degrees and BC¯¯¯¯¯¯¯¯=8. The second triangle has the vertices E, F and D. m<F = 65 degrees and m<D = 45 degrees. DE¯¯¯¯¯¯¯¯=8. Are the two triangles congruent and if yes, how do you know? Which segment is congruent to AB¯¯¯¯¯¯¯¯ (1 point) Responses
Yes by SAS, ED¯¯¯¯¯¯¯¯
Yes by SAS; EF¯¯¯¯¯¯¯¯
No, the triangles are not congruent
Yes by ASA; ED¯¯¯¯¯¯¯¯
The correct answer is:
No, the triangles are not congruent.
None of the given options show the correct congruence criterion for the two triangles.
The correct answer is:
Yes by ASA; EF¯¯¯¯¯¯¯¯
wait sorry I missed one of the answers, here you go
There are two triangles. For the first triangle, the vertices are A, B and C. m<A =65 degrees, m<B=70 degrees and BC¯¯¯¯¯¯¯¯=8. The second triangle has the vertices E, F and D. m<F = 65 degrees and m<D = 45 degrees. DE¯¯¯¯¯¯¯¯=8. Are the two triangles congruent and if yes, how do you know? Which segment is congruent to AB¯¯¯¯¯¯¯¯ (1 point) Responses
Yes by SAS, ED¯¯¯¯¯¯¯¯
Yes by SAS; EF¯¯¯¯¯¯¯¯
No, the triangles are not congruent
Yes by ASA; ED¯¯¯¯¯¯¯¯
Yes by ASA; EF¯¯¯¯¯¯¯¯
To determine if the two triangles are congruent, we can use the SAS (Side-Angle-Side) or ASA (Angle-Side-Angle) congruence criteria. Let's analyze the given information:
For the first triangle ABC with angles A = 65° and B = 70°:
- The length of BC is given as 8.
For the second triangle EFD with angles F = 65° and D = 45°:
- The length of DE is given as 8.
To apply the SAS congruence criteria, we need to have two sides and the included angle in both triangles congruent.
Looking at the given segments:
- From the first triangle ABC, there is no segment mentioned that is congruent to AB.
- From the second triangle EFD, the segment DE is congruent to AB in the first triangle.
Therefore, we can conclude that the two triangles are NOT congruent since only one pair of sides and an included angle are congruent in both triangles.
So, the correct answer is: No, the triangles are not congruent.