Question

in figure 12. 32' it is given that AB = DC and AC = DB

A) state the three pair of equal parts in the triangle ∆ABC and ∆DCB.

B) Is ∆ ABC is congruence to ∆DCB? Give reason.​

Answer 1

In above's figure

Given that

AC = DB

AB = DC

$\angle$ ABC = 90° = $\angle$DCB

Now

( A.) Three pairs of equal parts .

AC = DB (given)

AB = DC (given)

BC = BC (common)

( B.)

Yes ∆ ABC is congruent to ∆ DCB

via SSS criteria of congruency

as

AC = DB (given)

AB = DC (given)

BC = BC (common)

Also it is congruent by SAS criteria of congruency .

as

AC = DB

$\angle$ ABC = 90° = $\angle$DCB

AB = DC

Hope it helps you