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polet [3.4K]
3 years ago
15

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

Mathematics
1 answer:
loris [4]3 years ago
6 0

Answer:

∠ 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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