Quadrilaterals | Properties of Parallelogram | Parallelogram Theorems proof

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

Important properties of parallelograms:

Property of Parallelogram 1:Opposite sides are equal .

Property of Parallelogram 2:Opposite angels are equal.

Property of Parallelogram 3:Consecutive angles are supplementary .

Property of Parallelogram 4:If one angle is right, then all angles are right.Then,Parallelogram is a rectangle.

Important property of Parallelogram : The diagonals of a parallelogram bisect each other.That is, each diagonal passes through mid-point of other.

00:02 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q1 The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.

00:59 Apply Angle Sum Property of a Quadrilateral: It states that Sum of the angles of a quadrilateral is 360°.

03:00 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q2If the diagonals of a parallelogram are equal, then show that it is a rectangle.

04:12 Proof

05:05 Apply SSS congruency Rule

06:24 Apply properties of parallel lines.

07:34 Rectangle

07:57 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q3. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

09:40 Proof

10:30 Apply SAS congruency rule

13:30 Apply Properties of Rhombus

13:54 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q4. Show that the diagonals of a square are equal and bisect each other at right angles.

16:25 Use SAS congruency rule

17:32 Use of rule Vertically opposite angles are equal.

18:00 Use parallel lines property:Alternate interior angles are equal

23:21 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals Q5. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

24:48 Consider two triangles and find similarity between triangles.

28:12 Aplly property of Rhombus

29:03 Use property of Rhombus:The diagonals of a rhombus bisect each other at right angles (90°)

31:53 Apply parallel lines theorem:The sum of co-interior angles is 180

33:23 CBSE class 9 maths NCERT Solutions chapter 8 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.

35:04 Apply property of parallelogram: Opposite sides are equal & Opposite angels are equal

36:35 Use property of angular bisector: angular bisector is a line segment that divides the angle into two equal parts.

37:57 Use property of Isosceles Triangle Theorem:If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

38:57 CBSE class 9 maths NCERT Solutions chapter 8 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.

40:38 Proof

41:53 Apply SSS congruency rule

43:28 Property of Rhombus:In a Rhombus,Each diagonal bisect a pair of opposite angles.

45:11 CBSE class 9 maths NCERT Solutions chapter 8 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.

45:50 Property of Rectangle:In Rectangle,Each pair of opposite sides are equal.Each angle is a right angle.

46:25 Apply property of angular bisector: angular bisector is a line segment that divides the angle into two equal parts.

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