This is my first question here.
I have an exam tomorrow, please give me some good answers TT because I'm giving you guys 20 points
ignore this if you don't know the answer or I'll report you
Question:
Prove that if two sides and a median bisecting the third side of a triangle are respectively proportional to the corresponding sides and the median of another triangle, then the two triangles are similar.
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Answer:
Given :
△ABC and △PQR in which AL and PM are themedians such that,
PQ
AB
=
QR
BC
=
PM
AL
To prove :
△ABC∼△PQR
Proof :
PQ
AB
=
QR
BC
=
PM
AL
[ Given ]
As we know that a median bisects a side into two equal parts.
⇒ BL=LC and QM=MR
⇒ BC=2BL and QR=2QM
∴
PQ
AB
=
2QM
2BL
=
PM
AL
⇒
PQ
AB
=
QM
BL
=
PM
AL
⇒ △ABC∼△PQM [ By SSS similarity test ]
⇒ ∠B=∠Q [ C.P.S.T ]
Now, In △ABC∼△PQR, we have
⇒
PQ
AB
=
QR
BC
and ∠B=∠Q
∴ △ABC∼△PQR [ SAS similarity test ]
solution
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