he figure below shows two triangles. Which statement about the triangles is true?
i.imgsafe(.)org/c6dcf267d1.jpg
The triangles are congruent by:
1. AAS<<<
2. ASA
3. SAS
4. They are not congruent
2 angles and the contained side of one triangle are the same as 2 angles and the same contained side of another, so
ASA makes them congruent.
Based on the given figure, the correct statement about the triangles is option 3: SAS (Side-Angle-Side).
To determine if the triangles are congruent, we need to compare their corresponding sides and angles. Let's analyze the given figure:
The given triangles have two pairs of congruent angles: the angle at the top left corner (denoted as ∠A) and the angle at the top right corner (denoted as ∠B). These angles are clearly the same in both triangles.
Now, we need to compare the sides of the triangles. Looking at the figure, we can identify that the side opposite to ∠A in both triangles is of equal length, denoted as side a. However, the sides that are adjacent to ∠A have different lengths: in the left triangle, this side is longer, while in the right triangle, it is shorter.
By comparing the sides and angles, we find that the triangle on the left is NOT congruent to the triangle on the right using the condition of AAS (Angle-Angle-Side). In AAS congruence, we need to have two pairs of congruent angles and a congruent side between them. However, in this case, the side adjacent to one of the congruent angles is not congruent.
Therefore, the correct statement is: 4. They are not congruent.