Lesson 9-2: Congruence and Corresponding Parts

Property

Congruent sides are marked with identical tick marks, and congruent angles are marked with identical arc symbols. Equal numbers of marks indicate equal measures.

Examples

• In an isosceles triangle with two equal sides, mark both equal sides with single tick marks (|) and leave the third side unmarked.
• In an equilateral triangle, mark all three sides with single tick marks (|) and all three 60° angles with single arcs.
• In a right triangle with two equal legs, mark the equal sides with double tick marks (||) and mark the two 45° angles with single arcs.

Explanation

Mathematical notation uses visual symbols to clearly identify which parts of a triangle are congruent without requiring explicit numerical measurements. Tick marks on sides and arcs on angles with the same number of marks indicate those parts have equal measures. Proper marking is essential for setting up geometric proofs and "reading" a diagram correctly.

Property

In congruent figures, corresponding parts are the matching angles and sides that occupy the same relative positions.

A congruence statement ($\Delta ABC \cong \Delta DEF$) is valid if and only if the vertex order perfectly reflects the actual correspondence: