Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to ∆ ABC in which PQ = 8 cm. Also justify the construction.
Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD’ C’ similar to ∆BDC with scale factor 4/3 . Draw the line segment D’A’ parallel to DA where A’ lies on extended side BA. Is A’BC’D’ a parallelogram?
Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = 3/4 AB and AQ = 1/4 AC . Join P and Q and measure the length PQ.
Given a rhombus ABCD in which AB = 4 cm and ∠ABC = 60°, divide it into two triangles say, ABC and ADC. Construct the triangle AB’C’ similar to ∆ABC with scale factor 2/3 . Draw a line segment C’D’ parallel to CD where D’ lies on AD. Is AB’C’D’ a rhombus? Give reasons.
Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.
Draw a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm. Construct a triangle similar to it and of scale factor 5/3.
Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor 2/3 . Is the new triangle also a right triangle?
Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.