Question

in the given figure ac=bc angle dca=angle ecb and angle dbc= angle eac prove that dc=ec​

Answer 1

Answer:

in triangle ACE and triangle BCD

AC = BC ( given)

angle DCA = angle ECB ( given )

angle DBC = angle EAC ( given )

hence, triangle ACE is congruent to triangle BCD by ASA congruence rule..

so DC = EC ( by CPCP )

Step-by-step explanation:

Hope it'll surely help you....bbye

Answer 2

$\huge\underline\mathfrak\red{Answer:}$

We have

$\angle$DCA = $\angle$ECB.....1.

Adding $\angle$DCE to both sides of (1), we get

$\angle$DCE + $\angle$DCA = $\angle$DCE + $\angle$ECB

$\angle$ACE = $\angle$DCB......2.

______________________

In ∆EAC and ∆DBC, we have

• $\angle$ACE = $\angle$DCB
• AC = BC
• $\angle$EAC = $\angle$DAC.

1st one (from 2)

2nd (given)

3rd (given)

_______________________

So, by ASA-criterion of congruence, we have

∆EAC $\cong$ ∆DBC

$\implies$EC = DC