Скачать или смотреть Chapter 8 Quadrilaterals | Exercise 8.1 | Class 9 Maths NCERT Question Detailed Explanation

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✅ In this video,
✔️ Class: 9th
✔️ Subject: Maths
✔️ Chapter: 8 Quadrilaterals
✔️ Topic Name: Exercise 8.1

✔️ कक्षा: 9वीं
✔️ विषय: गणित
✔️ अध्याय: 8 चतुर्भुज
✔️ विषय का नाम: अभ्यास 8.1
✔ kaksha: 9veen
✔ vishay: ganit
✔ adhyaay: 8 : chaturbhuj
✔ vishay ka naam: abhyaas 8.1

Question Covered :-
1. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
4. Show that the diagonals of a square are equal and bisect each other at right angles.
5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
6. Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig. 8.19). Show that(i) it bisects ∠C also,(ii) ABCD is a rhombus.
7. ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
8. 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.
9. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that:(i) ΔAPD ≅ ΔCQB(ii) AP = CQ(iii) ΔAQB ≅ ΔCPD(iv) AQ = CP(v) APCQ is a parallelogram
10. ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that(i) ΔAPB ≅ ΔCQD(ii) AP = CQ
11. In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22).Show that (i) quadrilateral ABED is a parallelogram(ii) quadrilateral BEFC is a parallelogram(iii) AD || CF and AD = CF(iv) quadrilateral ACFD is a parallelogram(v) AC = DF(vi) ΔABC ≅ ΔDEF.
12. ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that (i) ∠A = ∠B (ii) ∠C = ∠D (iii) ΔABC ≅ ΔBAD(iv) diagonal AC = diagonal BD[Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

1. The angles of a quadrilateral are in the ratio 3 is to 5 is to 9 is to 13. Find all the angles of the quadrilateral.
2. If the diagonals of a parallelogram are equal, then show that it is a rectangle.
3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
4. Show that the diagonals of a square are equal and bisect each other at right angles.
5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
6. Diagonal A C of a parallelogram A B C D bisects angle A. Show that:
(i) it bisects angle C also,
(ii) A B C D is a rhombus.
7. A B C D is a rhombus. Show that diagonal A C bisects angle A as well as angle C, and diagonal B D bisects angle B as well as angle D.
8. A B C D is a rectangle in which diagonal A C bisects angle A as well as angle C. Show that:
(i) A B C D is a square,
(ii) diagonal B D bisects angle B as well as angle D.
9. In parallelogram A B C D, two points P and Q are taken on diagonal B D such that D P equals B Q. Show that:
(i) triangle A P D is congruent to triangle C Q B,
(ii) A P equals C Q,
(iii) triangle A Q B is congruent to triangle C P D,
(iv) A Q equals C P,
(v) quadrilateral A P C Q is a parallelogram.
10. A B C D is a parallelogram, and A P and C Q are perpendiculars from vertices A and C to diagonal B D. Show that:
(i) triangle A P B is congruent to triangle C Q D,
(ii) A P equals C Q.
11. In triangles A B C and D E F, A B equals D E, A B is parallel to D E, B C equals E F, and B C is parallel to E F. Vertices A, B, and C are joined to vertices D, E, and F respectively. Show that:
(i) quadrilateral A B E D is a parallelogram,
(ii) quadrilateral B E F C is a parallelogram,
(iii) A D is parallel to C F and A D equals C F,
(iv) quadrilateral A C F D is a parallelogram,
(v) A C equals D F,
(vi) triangle A B C is congruent to triangle D E F.
12. A B C D is a trapezium in which A B is parallel to C D and A D equals B C. Show that:
(i) angle A equals angle B,
(ii) angle C equals angle D,
(iii) triangle A B C is congruent to triangle B A D,
(iv) diagonal A C equals diagonal B D.
Hint: Extend A B and draw a line through point C parallel to D A, intersecting extended A B at point E.