Question

As shown in the fig. 3.39 side AB and side CD intersect each other at point O such that seg CO $\cong$ seg OB and $\angle$ACO $\cong$ $\angle$DBO.
Then show that $△$ACO $\cong$ $△$DBO and state remaining congruent parts.

Answer 1

Given: seg CO $\cong$ seg OB
and $\angle$ACO $\cong$ $\angle$DBO

Now, in $∆$ACO and $∆$DBO,
$\angle$ACO $\cong$ $\angle$DBO (given)
seg OC $\cong$ seg OB (given)
$\angle$AOC $\cong$ $\angle$DOB (vertically-opposite angles)
So,$∆$ACO $\cong$ $∆$DBO (ASA congruency test)
Then,
$\angle$OAC $\cong$ $\angle$ODB (c.a.c.t)
seg AC $\cong$ seg DB (c.s.c.t)
seg AO $\cong$ seg DO (c.s.c.t)