Question

Given: angle BCA and angle DCA are right angles; Segment BC and segment CD are congruent

Prove: angle B is congruent to angle D

Answer 1

∠ ABC = ∠ ADC proved

Explanation:

Between the triangles Δ BCA and Δ DCA,

(i) CA side is common for both the triangles.

(ii) ∠ ACB = ∠ ACD = 90° {Since Δ BCA and Δ DCA are right triangles}

(iii) Segment BC = Segment CD {Given}

Therefore, from Side-Angle-Side rule Δ BCA ≅ Δ DCA.

Therefore, ∠ ABC = ∠ ADC {Since they are corresponding angles of Δ BCA and Δ DCA. (Proved)