Q 1 – ABC is an isosceles triangle in which AB = AC. AD bisects exterior
angle PAC and CD || AB . Show that (i) ∠ DAC = ∠ BCA and (ii) ABCD is a parallelogram.
Q 2 – Show that the bisectors of angles of a parallelogram form a rectangle .
Q 3 – Diagonal AC of a parallelogram ABCD bisects ∠ A . Show that
(i) it bisects ∠ C also,
(ii) ABCD is a rhombus.
Q 5 – ABCD is a trapezium in which AB || CD and AD = BC .Show that
(i) ∠ A = ∠ B
(ii) ∠ C = ∠ D
(iii) ∆ ABC ≅ ∆ BAD
(iv) diagonal AC = diagonal BD
Q 6 – ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
Q 7 – In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively . Show that the line segments AF and EC trisect the diagonal BD.
Q 8 – ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i) D is the mid-point of AC
(ii) MD ⊥ AC
