Question

which of the following correctly describes triangle $abc$ from the image? it is smaller than triangle abc it is reflected over the y - axis it has larger angles than triangle abc it is congruent to triangle abc

Explanation:

Step1: Recall the definition of congruent triangles

Congruent triangles have the same shape and size, which means all corresponding sides and angles are equal.

Step2: Analyze the transformation

Looking at the graph, triangle \(A'B'C'\) is a translation (slide) of triangle \(ABC\). Translation is a rigid transformation. Rigid transformations (translations, rotations, reflections) preserve the shape and size of the figure.

Step3: Check other options

• If it was smaller (a dilation, a non - rigid transformation), side lengths would change. But there is no indication of a dilation.
• If it was reflected over the \(y\) - axis, the \(x\) - coordinates of corresponding points would have opposite signs. For example, if a point \((x,y)\) in \(ABC\) was reflected over the \(y\) - axis, it would be \((-x,y)\) in the image. But from the graph (assuming coordinates: if \(ABC\) has points like \((1,1),(2,3),(3,1)\) and \(A'B'C'\) has \((4,1),(5,3),(6,1)\)), it's a translation (not a reflection over \(y\) - axis).
• Angles of congruent triangles (formed by rigid transformations) are equal. So the statement “It has larger angles than triangle \(ABC\)” is false.

Answer:

It is congruent to triangle \(ABC\)