Geometric Proofs Math Example 3

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Example 3

easy
Prove that vertical angles are equal. Given: Lines ABAB and CDCD intersect at OO; prove ∠AOC=∠BOD\angle AOC = \angle BOD.

Solution

  1. 1
    ∠AOC+∠AOD=180°\angle AOC + \angle AOD = 180° (angles on a straight line CDCD).
  2. 2
    ∠BOD+∠AOD=180°\angle BOD + \angle AOD = 180° (angles on a straight line ABAB).
  3. 3
    Therefore ∠AOC=∠BOD\angle AOC = \angle BOD (both equal 180°−∠AOD180° - \angle AOD).

Answer

∠AOC=∠BOD\angle AOC = \angle BOD (vertical angles are equal).
Both vertical angles are supplementary to the same angle. When two quantities each equal the same third quantity, they are equal to each other — a straightforward deduction that appears throughout geometry proofs.

About Geometric Proofs

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

Learn more about Geometric Proofs →

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 4 medium

Given that [formula], prove that the perimeters are equal.

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