Two line segments AB and AC include an angle of \(60^o\) where AB = 5 cm and AC = 7 cm.  Locate points P and Q on AB and AC, respectively such that \(AP={3\over 4}\) AB and \(AQ={1\over 4}AC.\) Join P and Q and measure the length PQ.

4

(a)

Draw an isosceles triangle ABC in which AB = AC = 6cm and BC = 5cm. Construct a triangle PQR similar to \(\triangle ABC\) in which PQ = 8cm.  Also justify the construction.

4

(a)

Draw two tangents from the end points of the diameter of a circle of radius 4.0 cm. Are these tangents parallel?

4

(a)

Draw a \(\triangle\)ABC with BC = 7 cm, \(\angle B=45°\)  and \(\angle C=60°\). Then, construct another triangle, whose sides are \(\frac { 3 }{ 5 } \)  times of the corresponding sides of \(\Delta ABC\) and justify your construction.

4

(a)

Draw a right-angled triangle, in which the sides (other than the hypotenuse) are lengths 8 cm and 6 cm. Then, construct another triangle, whose sides are \(\frac { 3 }{ 4 } \)  times of the corresponding sides of  given triangle. Justify your construction.

4

(a)

Draw a \(\Delta ABC\), in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to \(\Delta ABC\) with scale factor 3/2. Justify the construction. Are the two triangles congruent? Note that all three angles and two sides of the two triangles are equal.

4

(a)

Construct a \(\Delta ABC\) , in which BC = 5cm, \(\angle CAB=120°\)and \(\angle ABC=30°\) . Then, construct another triangle whose sides are \(\frac{4}{5}\)times of the corresponding sides of \(\Delta ABC\) . Justify your construction.

4

(a)

To a circle of radius 4 cm, draw two tangents which are inclined to each other at an angle of 60°.

4

(a)

Construct a right triangle whose hypotenuse and one side measures 10 cm and 8 cm respectively. Then construct another triangle whose sides are \(\frac { 4 }{ 5 } \) times the corresponding sides of this triangle

4

(a)

Draw triangle ABC such that BC = 5 cm, corresponds to MBC with A'B :AB = 3 : 2.

4

(a)