Question

triangle abc and dbc have bc common ab= bd and ac = cd are the two triangles congruent state in symbolic form .which congruence condition do you use does angle and equals to angle and why or why not​

Answer 1

Answer:

Triangles ABC and DBC have side BC common, AB=BD and AC=CD.

So,

BC=BC⋯⋯[common side]

AB=BD⋯⋯[given]

AC=CD⋯⋯[given]

So, by SSS test we can say that,

ΔABC≅ΔDBC

Congruence condition used is SSS

Suppose congruent triangles are as shown as in the figure.

Then, ∠ABD



=∠ACD

Then they will not be equal.

Because , ∠ABD=∠ABC±∠DBC

and ∠ACD=∠ACB±∠DCB

From congruency, ∠ABC≅∠DBC and ∠ACB≅∠DCB

So, we cannot say that ∠ABD is equal to ∠ACD

hope it's help you

Answer 2

Answer:

Triangles ABC and DBC have side BC common, AB=BD and AC=CD.

So,

BC=BC⋯⋯[common side]

AB=BD⋯⋯[given]

AC=CD⋯⋯[given]

So, by SSS test we can say that,

ΔABC≅ΔDBC

Congruence condition used is SSS

Suppose congruent triangles are as shown as in the figure.

Then, ∠ABD



=∠ACD

Then they will not be equal.

Because , ∠ABD=∠ABC±∠DBC

and ∠ACD=∠ACB±∠DCB

From congruency, ∠ABC≅∠DBC and ∠ACB≅∠DCB

So, we cannot say that ∠ABD is equal to ∠ACD

solution