Question

ABC and DBC are two isosceles triangle on the same base BC show that angle ABD = angle ACD
see the figure given above

Answer 1

Hey friend.....here's it answer.

As the two triangles are isosceles so ab=ac.also bd=dc

Construct a line joining angle a to angle d.

So in triangle abd and triangle acd,

ab=ac

bd=dc

Ad is common

Thus the two triangles are congruent by sss

So,angle abd and angle acd is equal by cpct.

Hope this helps.

Plz mark it as brainliest✌✌✌

Answer 2

$<b> <I>$
Hey there!!

=> Given :-)

→ ABC is a isosceles triangle.

→ DBC is a isosceles triangle.

→ Both triangles are on the same base BC.

$\bf{ => To \: Prove :- \angle ABD = \angle ACD }$

=> Proof:-)

▶ In ∆ABC,

=> AB = AC. [ ABC is a isosceles triangle. ]

Then,

$\bf{ => \angle ABC = \angle ACB. ............(1). }$

[ Angle opposite to equal sides are equal ].

➡ Again,

▶ In ∆DBC,

=> DB = DC. [ DBC is a isosceles triangle. ]

Then,

$\bf{ => \angle DBC = \angle DCB ..............(2). }$

[ Angle opposite to equal sides are equal ].

➡ On adding equation (1) and (2), we get

$\bf{ => \angle ABC + \angle DBC = \angle ACB + \angle DCB . }$

=> $\huge \boxed{ => \angle ABD = \angle ACD . }$

✔✔ Hence, it is proved ✅✅.

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$\huge \boxed{ \mathbb{THANKS}}$

$\huge \bf{ \# \mathbb{B}e \mathbb{B}rainly.}$