Question

In the given figure.
(i) Are DABC and DDCB congruent?
(ii) Are DAOB congruent to DDOC?
Also identify the relation between corresponding elements and give reason for your answer.

Answer 1

aob is congurent prof

Answer 2

Answer:

ΔABC and ΔDCB congruent

ΔAOB congruent to ΔDOC

Step-by-step explanation:

in Δ ABC

∠BAC = 30°  

∠ACB = 50°

=> ∠ABC = 180° - ∠BAC - ∠ACB

=> ∠ABC = 180° -30° -  50°

=> ∠ABC = 100°

Similarly in Δ DCB

∠DCB = 100°

Δ ABC ≈  Δ DCB

but BC is common

=> Δ ABC ≅  Δ DCB

=> ΔABC and ΔDCB congruent

=> AB = DC

∠OAB = ∠ODC = 30°

∠OCD = ∠BCD - ∠BCO  = 100° - 50° = 50°

similarly ∠OBA     = 50°

∠OBA = ∠OCD  

Δ AOB ≅  Δ DOC

ΔAOB congruent to ΔDOC