Geometric Proofs Math Example 4

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Example 4

medium
Given that △ABC≅△DEF\triangle ABC \cong \triangle DEF, prove that the perimeters are equal.

Solution

  1. 1
    From congruence △ABC≅△DEF\triangle ABC \cong \triangle DEF: corresponding sides are equal, so AB=DEAB = DE, BC=EFBC = EF, CA=FDCA = FD.
  2. 2
    Perimeter of △ABC=AB+BC+CA\triangle ABC = AB + BC + CA; perimeter of △DEF=DE+EF+FD\triangle DEF = DE + EF + FD.
  3. 3
    Substituting the equal pairs: perimeter of △DEF=AB+BC+CA\triangle DEF = AB + BC + CA = perimeter of △ABC\triangle ABC.

Answer

The perimeters are equal.
Congruent triangles have all corresponding parts equal (CPCTC). Since the perimeter is the sum of the three sides, substituting the equal corresponding sides shows the perimeters must be equal.

About Geometric Proofs

Geometric proofs establish that a geometric claim is true by chaining justified statements from definitions, theorems, and givens.

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More Geometric Proofs Examples

Example 1 medium

Prove that the base angles of an isosceles triangle are equal.

Example 2 hard

Prove by contradiction: if two lines are cut by a transversal so that alternate interior angles are

Example 3 easy

Prove that vertical angles are equal. Given: Lines [formula] and [formula] intersect at [formula]; p

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