Question

triangles ABC and DBC have side BC common, AB = BD and AC = CD .are the two triangles congruent state in symbolic form which congruent condition do you use ? Does angle ABD = ACD why or why not ?​

Answer 1

Yes , Both are congruent

symbolic form :- ∆BAC = ∆BDC

Yes angle ABD = ACD because of C.P.C.T means corresponding parts of congruent triangles

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Answer 2

$\Large\underline{\underline{\green{\sf Question \;}}}$

Triαngles ABC αnd DBC hαve side BC common, AB = BD αnd AC = CD. Are the two triαngles congruent? Stαte in symbolic form. Which congruence condition do you use? Does ∠ABD equal ∠ACD? Why or why not?

$\Large\underline{\underline{\green{\sf Required\; Solution:}}}$

Yes.

In ΔABC αnd ΔDBC

AB = DB

• Given

AC = DC

• Given

BC = BC

• Common

By SSS criterion of congruency, ΔABC ≅ ΔDBC    

No, ∠ABD and ∠ACD αre not equαl

, becαuse AB ≠ AC.

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Hope it elps! :)