Qn 1.

a) Write the measure of ∠A.

b) Find the length of PQ?

Qn 2.

In the figure, triangle ABC is an equilateral triangle. P,Q,R are the mid points of the sides AB,BC, CA respectively.

a) Find the measures of the angles of triangle PBQ

b) Find the measures of the angles of triangle PQR

c) Prove that the lengths of the sides of triangle PQR are half the lengths of sides of triangle ABC.

Qn 3.

In the figure ABCD is a parallelogram. QC=2BQ.

a) Prove that triangles PQB and CQD are similar.

b) How many times the sides of triangle PBQ are the sides of triangle CQD.

c) Find another pair of similar triangles from the figure.

Qn 4.

In the figure PQ is parallel to BC and PR is parallel to CD

a) Write the equal angles of triangles AQP and ABC

b) Write the equal angles of triangles ARP and ADC

c) Prove that =

Qn 5.

In triangle ABC, CP and BQ are perpendicular to the sides AB and AC respectively.

a) If ∠A=x°, find the measures of ∠ABQ and ∠ACP.

b) Write the ratios of the sides opposite to the equal angles in triangle AQB and triangle APC

c) Prove that AP x AB = AQxAC

Qn 6.

In triangle ABC, ∠B=90°. BD is perpendicular to AC.

a) If ∠A=x° , find the measures of ∠C and ∠ABD .

b) Write the ratios of the sides opposite to the equal angles in triangle ABD and triangle ABC

c) Prove that = AD x AC