Question

Which descriptions from the list below accurately describe the relationship between ABC and DEF? Check all that apply.

A. Same area
B. Same size
C. Congruent
D. None of the above

Answer 1

The correct answer is D) none of the above.

Explanation:
The angles are the same but the side lengths are different. This means that they are not the same size, which also means they are not congruent.

It also means the area is not the same, which can be verified using the area formula: A=1/2bh=1/2(3)(4)=6 for the smaller triangle, and A=1/2bh=1/2(6)(8)=24 for the larger one.

Answer 2

Answer:

(D) None of the above

Step-by-step explanation:

Since, from the given figure, ∠A=∠D, ∠B=∠E and ∠C=∠F, but the corresponding sides that are AB,ED,AC,DF,BC,EF are not equal, which means that both the triangles does not have same size.

Since, Angles of both triangles are equal but sides are not equal, therefore both the triangles cannot be congruent.

Now, Area of triangleABC= $\frac{1}{2}{\times}3{\times}4=6$ and area triangleDEF= $\frac{1}{2}{\times}6{\times}8=24$

Since, both the area also do not have their areas same, therefore none of the above describes the relationship between triangle ABC and DEF.

Therefore, Option D is correct.