How to prove Quadrilaterals are Parallelograms using Properties 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 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).
(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.
35:15 Apply property of parallelogram:In a parallelogram, pair of opposite sides are equal.
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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