In `Delta ABC, AB = 1, BC = 1, and AC = 1//sqrt2`. In `Delta MNP, MN =1, NP =1, and angle MNP = 2 angle ABC`. Find the side MP

In triangle ABC, angle ABC =90^@ angle BAC =45^@ and AC =4 sqrt(2) cm , then find AB.

In Delta MNP,NQ is a bisector of angle N. If MN = 5, PN = 7, MQ = 2.5 ,then find QP

In triangle ABC, AB = (2a-1)cm, AC = 2sqrt(2a) cm, BC = (2a+1)cm, find angle BAC .

In the triangle ABC, BC = m^2 -n^2 , AC =3 mn and AB = m^2+n^2 . Prove that it is a right angled triangle.

In Delta ABC, M and N are points on the sides AB and AC respectively such that BM=CN . If angle A= angle C then show that MN||BC .

Draw a Delta ABC with AB= 4 cm, BC = 9 cm and AC = 6 cm. Then construct a triangle similar to Delta ABC whose sides are 1 (1)/(2) times the corresponding sides of Delta ABC.

In a Delta ABC , D is the mid point of side AC such that BD =1/2 AC . Show that angleABC is a right angle.