In `triangleABC`, `angleA=30^o`, `angleB=40^o` and `angleC=110^o`. In `trianglePQR`, `angleP=30^o`, `angleQ=40^o` and `angleR=110^o`. A student says that `triangleABC` `~=` `trianglePQR` by AAA congruence. Is he justified? Why or why not?

Construct trianglePQR if PQ=5cm, mlfloorPQR=105^o and mlfloorQRP=40^o (Hint: Recall angle sum property of a traingle).

In the figure ,AB tangent to the circle with centre O.If angleAOB=30^(@) ,then angleA and angleB respectively are:

If a quadrilateral ABCD, the bisector of angleC angleD intersect at O. Prove that angleCOD=(1)/(2)(angleA+angleB)

In an isosceles ABC, with AB = AC, the bisectors of angleB and angleC intersect each other at O. Joint A to O. Show that: (ii) OB = OC (ii) AO bisects angleA

A man wishes to estimate the distance of a nearby tower from him. He stands at a point A in front of the tower C and spots a very distant object O in line with AC. He then walks perpendicular to AC up to B, a distance of 100 m, and looks at O and C again. Since O is very distant , the direction BO is practically the same as AO, but he finds the line of sight of C shifted from the original line of sight by an angle theta = 40^(@) ( theta is known as 'Parallax') estimate the distance of the tower C from his original position A.

The blood groups of 30 students of class VIII are recorded as follows : A,B,O,O,AB,O,A,O,B,A,O,B,A,O,O,A,AB,O,A,A,O,O,AB,B,A,O,B,A,B,O. Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students ?

The blood groups of 30 students of Class VIII are recorded as follows: {:(A",",B",",O",",O",",AB",",O",",A",",O",",B",",A","),(O",",B",",A",",O",",O",",A",",AB",",O",",A",",A","),(O",",O",",AB",",B",",A",",O",",B",",A",",B",",O):} Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students ?