Math, asked by Anonymous, 7 months ago

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.

Answers

Answered by Rushilmadia
1

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

Similar questions