Given: angle bca and angle dca are right angles; segment bc and segment cd are congruent
prove: angle b is congruent to angle d

∠ ABC = ∠ ADC proved

Step-by-step 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)

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step-by-step explanation:

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