Question

2.
In the adjacent figure.
(i) Are AAOB congruent to ADOC?
(2) Are AABC and ADCB congruent?
Also identify the relation between corresponding elements and
give reason for your answer.
​

Answer 1

Answer:

Consider ∆AOB and ∆DOC

angleAOB = angleDOC. (vertically opposite)

angleBAO = angleCDO =30°

As two angles are equal third angle must be equal by angle sum property.

In ∆OBC

As OBC is isosceles triangle

OB=OC (sides opposite to equal angle are equal)

So,

angleAOB = angleDOC. (vertically opposite)

angleABO = angleDCO. (from above)

OB=OC

∆AOB is congruent to ∆DOC by ASA congruence

AB=DC by CPCT

AO=OD by CPCT

Consider ∆ABC and ∆DCB

AB=AC

AO+OC=DO+OB

AC=BD

BC=BC (common)

So, ∆ABC is congruent to ∆DCB by SSS congruence

Hope you find my answer helpful

Please mark as brainliest