Question

In a figure, AB=BC and AD=DC. prove that : angle BAD = angle BCD​

Answer 1

Answer:

$\text{Solution:}\\\text{Given: AB = BC and AD = DC}\\\text{To prove: }\angle\text{BAD}=\angle\text{BCD}\\\text{Proof:}$

$\text{1. In triangles ABD and BCD,}\\\text{i. AB = BC (S) [Given]}\\\text{ii. AD = CD (S) [Given]}\\\text{iii. BD = BD (S) [Common side]}\\\text{iv. }\triangle\text{ABD}\cong\triangle\text{BCD}\ \ \ [\text{By S.S.S. axiom.}]$

$\text{2. }\angle\text{BAD}=\angle\text{BCD}\ \ \ [\text{Corresponding angles of congruent triangles are equal.}]$

$\text{}\qquad\text{proved}$