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Corresponding

Corresponding

Two features that are situated the same way in different objects.

Worked Example

Problem: Triangle ABC is similar to triangle DEF, where A corresponds to D, B corresponds to E, and C corresponds to F. If angle A = 50°, angle B = 60°, and side AB = 8 cm while side DE = 12 cm, find the corresponding angle D and the ratio of corresponding sides.
Step 1: Identify the corresponding angles. Since A corresponds to D, angle D must equal angle A.
∠D=∠A=50°\angle D = \angle A = 50°
Step 2: Identify the corresponding sides. Side AB corresponds to side DE because A↔D and B↔E.
AB↔DEAB \leftrightarrow DE
Step 3: Find the ratio of corresponding sides.
DEAB=128=32\frac{DE}{AB} = \frac{12}{8} = \frac{3}{2}
Answer: The corresponding angle D = 50°, and the ratio of corresponding sides is 3:2.

Why It Matters

Identifying corresponding parts is essential when working with congruent or similar figures. It tells you which angles are equal and which sides are proportional, enabling you to set up correct equations and solve for unknown measurements. The concept also appears when a transversal crosses parallel lines, creating corresponding angles that are equal.

Common Mistakes

Mistake: Matching corresponding parts by appearance rather than by their stated order or position.
Correction: Always use the order in which the figures are named. If triangle ABC ≅ triangle DEF, then A↔D, B↔E, and C↔F — regardless of how the triangles are drawn or oriented.

Related Terms

  • Congruent — Figures whose corresponding parts are all equal
  • Similar — Figures with equal corresponding angles and proportional sides
  • Corresponding Angles — Equal angles formed by a transversal and parallel lines
  • Parallel Lines — Create corresponding angles when cut by a transversal