Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD)
10. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC). 10. AB || The diagonals AC and BD of the isosceles ABCD containing DC intersect each other at point O. Prove that ar(AOD) = ar(BOC) 10. ab || dch vaale samalamb chaturbhuj abchd ke vikarn ach aur bd ek doosare ko bindu o par pratichchhed karate hain. siddh keejie ki ar (shore) = ar (mouth) Question 10: The diagonals AC and BD of a trapezium ABCD intersect each other at point O. The trapezium has AB parallel to DC (that is, AB ∥ DC). Prove that: The area of triangle A-O-D is equal to the area of triangle B-O-C. (That is: ar(AOD) = ar(BOC)) You can contact with us - / thestudyadda / thestudy01 Telegram- https://t.me/TheStudyAdda Video Link Chapter 9 Exercise 9.1- • Chapter 9 Areas of Parallelograms and Tria... Video Link Chapter 9 Exercise 9.2- • Chapter 9 Areas of Parallelograms and Tria... Video Link Chapter 9 Exercise 9.3- • Chapter 9 Areas of Parallelograms and Tria... Chapterwise Playlist of Class 9 Math NCERT - • CLASS 9th NCERT MATHS Chapterwise Solution... QuestionWise Playlist of Class 9th NCERT Math - • Class 9th NCERT Maths | All NCERT Mathemat... Class 9th NCERT CHAPTER 9 Areas of Parallelogram & Triangles Exercise 9.3 Questions 1. In Fig.9.23, E is any point on median AD of a ΔABC. Show that ar (ABE) = ar(ACE). 2. In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = 1/4 ar(ABC). 3. Show that the diagonals of a parallelogram divide it into four triangles of equal area. 4. In Figs. 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). 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) the(DEF) = 1/4 of(ABC)(iii) the (BDEF) = 1/2 of(ABC) 6. In Figs. 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.[Hint : From D and B, draw perpendiculars to AC.] 7. D and E are points on sides AB and AC respectively of ΔABC such that ar(DBC) = ar(EBC). Prove that DE || BC. 8. XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meets XY at E and F respectively, show thatar(ΔABE) = ar(ΔAC) 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).] 11. In Figs. 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) 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 amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented. 13. ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).[Hint : Join CX.] 14. In Fig.9.28, AP || BQ || CR. Prove that ar(AQC) = ar(PBR). 15. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium. 16. In Fig.9.29, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums. 1. aakrti 9.23 mein, ai ek dabch kee maadhyika ad par koee bindu hai. darshaie ki ar (abai) = ar(achai). 2. ek tribhuj abch mein, ai maadhyika ad ka madhy-bindu hai. darshaie ki ar(baid) = 1/4 ar(abch). 3. darshaie ki ek samaantar chaturbhuj ke vikarn use baraabar kshetraphal vaale chaar tribhujon mein vibhaajit karate hain. 4. aakrti 9.24 mein, abch aur abd ek hee aadhaar ab par sthit do tribhuj hain. yadi rekhaakhand chd ko ab dvaara o par samadvibhaajit kiya jaata hai, darshaie ki ar(abch) = ar(abd). 5. d, ai aur f kramashah ek dabch kee bhujaon bch, ch aur ab ke madhy-bindu hain. darshaie ki:- (i) bdaif ek samaantar chaturbhuj hai. (ii) or(daif) = 1/4 or(abch) (iii) or (bdaif) = 1/2 or(abch) 6. aakrti 9.25 mein, chaturbhuj abchd ke vikarn ach aur bd ek doosare ko bindu o par is prakaar pratichchhed karate hain ki ob = od. yadi ab = chd, to darshaie ki: (i) ar (doch) = ar (aob) (ii) ar (dchb) = ar (achb) (iii) da || chb ya abchd ek samaantar chaturbhuj hai. [sanket: d aur b se ach par lamb kenenchen.] 7. d aur ai kramashah dabch kee bhujaon ab aur ach par is prakaar bindu hain ki ar(dbch) = ar(aibch). siddh keejie ki dai || bch.
