two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their angular points are equal
Share
two isosceles triangles whose vertical angles are equal are placed so as to have their vertices coincide. prove that the line joining their angular points are equal
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
ANSWER
Let △ABC and △DEF be the given triangles such that AB=AC and DE=DF, ∠A=∠D
and
Area(△DEF)
Area(△ABC)
=
25
16
.......(i)
Draw AL⊥BC and DM⊥EF.
Now, AB=AC,DE=DF
⇒
AC
AB
=1 and
DF
DE
=1
⇒
AC
AB
=
DF
DE
⇒
DE
AB
=
DF
AC
Thus, in triangles ABC and DEF, we have
DE
AB
=
DF
AC
and ∠A=∠D [Given]
So, by SAS-similarity criterion, we have
△ABC∼△DEF
⇒
Area(△DEF)
Area(△ABC)
=
DM
2
AL
2
⇒
25
16
=
DM
2
AL
2
[Using (i)]
⇒
DM
AL
=
5
4
Hence, AL:DM=4:5
Step-by-step explanation:
inbox me