Chapter 9 – Areas of Parallelogram and Triangles

12. A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given equal [...]

11. In Fig. 9.27, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar(△ACB) = ar(△ACF) (ii) ar(AEDF) = ar(ABCDE) 11. In Fig. 9.27 ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar(△ACB) = [...]

10. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC). 10. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC). October 15, 2020 Category: Chapter [...]

9. The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed (see Fig. 9.26). Show that ar(ABCD) = ar(PBQR). [Hint : Join AC and PQ. Now compare ar(ACQ) and ar(APQ).] 5. In Fig. [...]

8. XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively, show that ar(ΔABE) = ar(ΔACF) 8. XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet [...]

7. D and E are points on sides AB and AC respectively of ΔABC such that ar(DBC) = ar(EBC). Prove that DE || BC. 7. D and E are points on sides AB and AC respectively of ΔABC such that ar(DBC) = ar(EBC). Prove that DE || BC. October 15, 2020 Category: Chapter 9 - [...]

6. In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that: (i) ar (DOC) = ar (AOB) (ii) ar (DCB) = ar (ACB) (iii) DA || CB or ABCD is a parallelogram. 6. In Fig. 9.25 diagonals AC and BD [...]

5. D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC. Show that (i) BDEF is a parallelogram. (ii) ar(DEF) = ¼ ar(ABC) (iii) ar (BDEF) = ½ ar(ABC) 5. D CA and AB of a ΔABC. Show that (i) BDEF is a parallelogram. (ii) ar(DEF) = [...]

4. In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD). 4. In Fig. 9.24 ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O [...]

3. Show that the diagonals of a parallelogram divide it into four triangles of equal area. 3. Show that the diagonals of a parallelogram divide it into four triangles of equal area. October 15, 2020 Category: Chapter 9 - Areas of Parallelogram and Triangles , Maths , NCERT Class 9 ,