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Prove That: (I) ∆ Abc ≅ ∆ Adc (Ii) ∠B = ∠D (Iii) Ac Bisects Angle Dcb - Mathematics

Sum

Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB

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Solution

Given: In the figure,
AB = AD, CB = CD

To prove: Δ ABC ≅ Δ ADC
∠B = ∠D

AC bisects angle DCB

Proof: In Δ ABC and Δ ADC,
AC = AC .............(common)
AB = AD .............(given)
CB = CD .............(given)

(i) ∴ Δ ABC ≅ Δ ADC .................(SSS aciom)

(ii) ∴ ∠B = D .................(c.p.c.t.)
∠BCA = ∠DCA

(iii) ∴ AC bisects ∠DCB

  Is there an error in this question or solution?
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APPEARS IN

Selina Concise Mathematics Class 7 ICSE
Chapter 19 Congruency: Congruent Triangles
Exercise 19 | Q 3
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