知识点 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.

核心知识

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.

深入理解

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.

题目

示例解析

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 $𝐸 𝐹$ ?

选择一个答案查看解析