Question

Model Question Paper Part -
The sides LM and LN of ALMN are congruent. MP and MQ are drawn from M to make
congruent angles with MN and meet LM and LN produced in points P and Q respectively.
LM LP
Prove that:LM sqaure/LQ sqaure=LP/LQ​

Answer 1

Theorem

If ABC is a triangle then <)ABC + <)BCA + <)CAB = 180 degrees.

Proof

Draw line a through points A and B. Draw line b through point C and parallel to line a.

triangle

Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'.

It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees.

Thus <)ABC + <)BCA + <)CAB = 180 degrees.