Concept 2

Apply similarity and congruence; use proportional reasoning in similar figures.

Similar figures use a constant scale factor, and congruent figures match side for side.

Core Idea

Congruent figures have equal corresponding parts. Similar figures have equal corresponding angles and side lengths in one constant scale factor, so match corresponding sides before writing any proportion.

Understanding

Rule: In similar figures, every pair of corresponding side lengths has the same ratio. That scale factor controls all linear measurements, while areas scale by the square of the factor. In congruent figures, the scale factor is $1$ , so corresponding sides and angles are equal.

On ACT, the main trap is not the arithmetic. It is pairing the wrong sides. Use the stated order of the vertices or mark matching angles first, then build the proportion in the same order on both sides.

Question

Worked Example

Triangle $𝐴 𝐵 𝐶$ is similar to triangle $𝐷 𝐸 𝐹$ . If $𝐴 𝐵 = 6$ , $𝐵 𝐶 = 8$ , and $𝐷 𝐸 = 9$ , what is the length of $𝐸 𝐹$ ?

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