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Solve the triangle 📐

Mathematics

ScanSolve AI Answer

Step-by-step solution

2 steps

To solve the triangle, we will use the properties of similar triangles and the Pythagorean theorem.

Assumptions:

  • The lines BEBE and CDCD are parallel, as indicated by the arrows.
  • The angle ∠A\angle A is a right angle (90∘90^\circ), as visually suggested by the diagram.
  1. Identify similar triangles.

    Since BE∥CDBE \parallel CD, the transversal lines ACAC and ADAD create corresponding angles.
    ∠ABE=∠ACD\angle ABE = \angle ACD
    ∠AEB=∠ADC\angle AEB = \angle ADC
    ∠BAE=∠CAD\angle BAE = \angle CAD (common angle)
    Therefore, △ABE∼△ACD\triangle ABE \sim \triangle ACD (by AAA similarity criterion).

  2. Calculate the length of

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