Quadrilaterals | Application of Properties of Parallelogram to solve problem

http://www.learncbse.in/ncert-solutions-for-class-9-maths/

A quadrilateral has four sides, four angles and four vertices.

In this chapter, we will study more about different types of quadrilaterals, their properties and especially those of parallelograms.

In this video, we learn how to apply Congruency Rule to solve Problems on Qudrilaterals. Use parallel lines concept and triangle congruence theorems to prove/solve problems on properties of parallelograms.

Reference book for the above video is

National Council of Educational Research and Training (NCERT) Book for Class 9 Subject: Maths

This Video is also refers as CBSE Class 9 mathts NCERT Solutions Chapter 8 Quadrilaterals

00:03 CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals q6 Diagonal AC of a parallelogram ABCD bisects Angle A (see Fig. 8.19). Show that

(i) it bisects Angle C also,

(ii) ABCD is a rhombus.

01:11 Apply property of parallelogram: Opposite sides are equal & Opposite angels are equal

03:33 Use property of angular bisector: angular bisector is a line segment that divides the angle into two equal parts.

04:28 Use property of Isosceles Triangle Theorem:If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

05:18 Property of Rhombus:All sides are equal

05:35 CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals q7 ABCD is a rhombus. Show that diagonal AC bisects Angle A as well as Angle C and diagonal BD bisects Angle B as well as Angle D.

07:10 Proof

08:28 Apply SSS congruency rule

11:22 Property of Rhombus:In a Rhombus,Each diagonal bisect a pair of opposite angles.

11:49 CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals q8 8. ABCD is a rectangle in which diagonal AC bisects Angle A as well as Angle C. Show that:

(i) ABCD is a square (ii) diagonal BD bisects Angle B as well as Angle D.

12:30 Property of Rectangle:In Rectangle,Each pair of opposite sides are equal.Each angle is a right angle.

13:00 Apply property of angular bisector: angular bisector is a line segment that divides the angle into two equal parts.

19:08 CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals q9 In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that:

(i) triangle APD congruent to triangle CQB

(ii) AP = CQ

(iii) triangle AQB congruent to triangle CPD

(iv) AQ = CP

(v) APCQ is a parallelogram

20:10 Apply property of parallelogram:In a parallelogram, pair of opposite sides are equal.

21:16 (i) (ii)

22:20 Apply Alternate Interior Angles Theorem: It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

23:43 (iii) (iv)

24:50 Use Alternate Interior Angles Theorem: It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

25:45 (v)

26:26 Use Linear Pair of angles:Two angles that are adjacent (share a leg) and supplementary (add up to 180°)

29:33 CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals Q10. 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) triangle APB congruent to triangle CQD

(ii) AP = CQ

30:44 Proof

31:15 Use property of parallelogram:In a parallelogram, pair of opposite sides are equal.

32:41 CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals q11 11. In triangle ABC and triangle DEF, 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) triangle ABC congruent to triangle DEF.

38:36 CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals q12 ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that

(i) Angle A = Angle B (ii) Angle C = Angle D (iii) triangle ABC congruent to triangle BAD (iv) diagonal AC = diagonal BD

39:21 Property of Trapezium states that it has only one pair of parallel sides.Non parallel sides are equal.

39:46 Construction to solve the problem

41:04 Isosceles Triangle Theorem. If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

42:48 Co-interior angles are inside the lines on the same side of the transversal. Whenever the pair of lines is parallel the co-interior angles add to 180.

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CBSE solutions for class 9 maths Quadrilaterals

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