Answer:
Given in figure ABCD:
∠ABD≅∠CBD
AB≅CB
To prove:
∠A≅∠C
Solution:
In the figure ABCD, we will first prove the Δ ABD and Δ CBD are congruent.
Thus the proof can be given as:
Statement Reason
1) [tex]\angle ABD \cong \angle CBD[/tex] Given
2) [tex]AB\cong CB[/tex] Given
3) [tex]BD\cong BD[/tex] Reflexive property of congruence (As the segment is congruent to itself)
4) [tex]\triangle ABD\cong \triangle CBD[/tex] S.A.S (Side Angle side)
5) [tex]\angle A\cong \angle C[/tex] Corresponding parts of congruent triangles are congruent.
Hence proved.
