Question

plz solve it and send me solutions

Answer 1

In the 10th one

lets take a rectangle or a parallelogram ABCD in which AC is the diagonal

in that:-

AB=CD  and  CB=AD ..................(Opposite sides of a rectangle or parallelogram are equal)

∠ABC=∠CDA..............(Angles of a rectangle or parallelogram are always 90°)

So by SAS criterion ΔABC≅CDA         which proves that the diagonal of  a rectangle or parallelogram divides it into two congruent triangles

In the 11th one:-

According to angle sum property

in ΔAOB.....∠A+∠B+∠O=180°

                   ∠A+47°+55°=180

                  ∠A+102°=180°

                  ∠A=180-102°

                  ∠A=78°

∠P must be equal to ∠A as the angles in ΔOPQ are similar to the angles of ΔOAB

∠P=∠A=78°

In ΔAOB and ΔPOQ

∠OAB=OPQ...........(proven by i)

OA=OP..............(given)

∠AOB=∠POQ.................(vertically opposite angle)

So by ASA criterion ΔAOB≅ΔPOQ

HOPE MY ANSWER HELPS YOU:)