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In figure 1.55, ∠ABC = 75°, ∠EDC = 75°. State which two triangles are similar and by which test? Also write the similarity of these two triangles by a proper one to one correspondence.

In figure 1.55, \(\angle ABC = 75^\circ\), \(\angle EDC = 75^\circ\). State which two triangles are similar and by which test? Also write the similarity of these two triangles by a proper one to one correspondence.

Figure: In \(\triangle ABC\), point D is on side AC and point E is on side BC (A–D–C, B–E–C); seg DE is drawn. \(\angle ABC = 75^\circ\) and \(\angle EDC = 75^\circ\).

1 answer

Answer: \(\triangle ABC \sim \triangle EDC\) by the AA test.

In \(\triangle ABC\) and \(\triangle EDC\):

  • \(\angle ABC \cong \angle EDC\) (each is \(75^\circ\), given)
  • \(\angle ACB \cong \angle ECD\) (common angle C)

Two angles of one triangle are congruent to two angles of the other, so by the AA test of similarity the triangles are similar.

Correspondence: A ↔ E, B ↔ D, C ↔ C. Hence \(\triangle ABC \sim \triangle EDC\).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report
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