How to prove Quadrilaterals are Parallelograms using Properties of Parallelograms

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

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 q2 If the diagonals of a parallelogram are equal, then show that it is a rectangle.

00:59 Proof , consider two triangles for similarity test.

01:54 Apply SSS congruency Rule

03:13 Apply properties of parallel lines.Co interior angles are supplementry.

04:28 In Rectangle, Each pair of opposite sides are equal. Each angle is a right angle.

04:48 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q8 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.

05:30 Property of Rectangle:In Rectangle,Each pair of opposite sides are equal.Each angle is a right angle.

06:07 Apply property of angular bisector: angular bisector is a line segment that divides the angle into two equal parts.

12:07 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.

13:55 Proof, consider two triangles for similarity test.

16:04 Apply SAS congruency rule

17:30 Apply Properties of Rhombus

18:04 q4 Show that the diagonals of a square are equal and bisect each other at right angles.

20:35 Use SAS congruency rule

21:40 Use of rule Vertically opposite angles are equal.

22:10 Use parallel lines property:Alternate interior angles are equal

23:34 Apply CPCT

27:30 CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals q11 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.

29:46 (i)

35:15 Apply property of parallelogram:In a parallelogram, pair of opposite sides are equal.

30:18 (ii)

30:49 (iii)

31:43 (iv)

32:36 (v) (vi)

33:24 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.

34:55 Consider two triangles and find similarity between triangles.

38:12 Aplly property of Rhombus

39:17 Use property of Rhombus:The diagonals of a rhombus bisect each other at right angles (90°)

41:55 Apply parallel lines theorem:The sum of co-interior angles is 180

43:05 Aplly properties of Square

43:28 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.

45:09 Apply property of parallelogram: Opposite sides are equal & Opposite angels are equal

16:40 Use property of angular bisector: angular bisector is a line segment that divides the angle into two equal parts.

48:00 Use property of Isosceles Triangle Theorem:If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

48:50 Property of Rhombus:All sides are equal

Properties of parallelograms that help to determine if a quadrilateral is a parallelogram

Proving that a Quadrilateral is a Parallelogram (Lesson)

Proving a Quadrilateral a Parallelogram | Geometry Proof How To Help

Proving Quadrilaterals are Parallelograms

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