9th NCERT MATHS_QUADRILATERAL_8.1-within 10 minutes, anyone can understand 8.1 exercise

1. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
2. Show that the diagonals of a square are equal and bisect each other at right angles.
3. Diagonal AC of a parallelogram ABCD bisects
∠ A (see Fig. 8.11). Show that
(i) it bisects ∠ C also,
(ii) ABCD is a rhombus.
4. ABCD is a rectangle in which diagonal AC bisects
∠ A as well as ∠ C. Show that: (i) ABCD is a square
(ii) diagonal BD bisects ∠ B as well as ∠ D.5. In parallelogram ABCD, two points P and Q are
taken on diagonal BD such that DP = BQ
(see Fig. 8.12). Show that:
(i) ∆ APD ≅ ∆ CQB
(ii) AP = CQ
(iii) ∆ AQB ≅∆ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram
6. ABCD is a parallelogram and AP and CQ are
perpendiculars from vertices A and C on diagonal
BD (see Fig. 8.13). Show that
(i) ∆ APB ≅ ∆ CQD
(ii) AP = CQ
7. ABCD is a trapezium in which AB || CD and
AD = BC (see Fig. 8.14). Show that
(i) ∠ A = ∠ B
(ii) ∠ C = ∠ D
(iii) ∆ ABC ≅ ∆ BAD#9ncert #9thmaths #9thncert #youtube #youtubesearch #youtubevideo #google #googleimagesearch #googleimages #rectangle #parallel_lines #parallelogram
(iv) diagonal AC = diagonal BD