Construct an isosceles triangle, given its base and base angle and justify the construction.

Construct an equilateral triangle, given its side of length of 4.5 cm and justify the construction.

Construct the following angles at the initial point of a given ray and justify the construction. (a) 90^(@) (b) 45^(@)

The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?

If in an isosceles triangle with base 'a', vertical angle 20^@ and lateral side each of length 'b' is given then value of a^3+b^3 equals

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find its length and breadth.

Construct an isosceles triangle PQR where PQ = PR and angleQ = 50^(@) , QR = 7 cm. Also draw its circumcircle.

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The area of quadrilateral which the straight line cuts off from the given triangle is

Construct the bisector of a given angle ABC.

The base of an isosceles triangle measures 4 units base angle is equal to 45^(@) . A straight line cuts the extension of the base at a point M at the angle theta and bisects the lateral side of the triangle which is nearest to M. The length of portion of straight line inside the triangle may lie in the range