Quadrilaterals | Properties of Parallelogram and their application to solve problems

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 q9 In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that:

00:52 Apply property of parallelogram:In a parallelogram, pair of opposite sides are equal.

02:08 (i) triangle APD congruent to triangle CQB (ii)AP = CQ

03:09 Apply Alternate Interior Angles Theorem: It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

04:00 Use SAS congruency rule

04:45 (iii) triangle AQB congruent to triangle CPD (iv) AQ = CP

05:42 Use Alternate Interior Angles Theorem: It states that when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

06:18 Apply CPCT (Corresponding Parts of Congruent Triangles)

06:56 (v) APCQ is a parallelogram

07:19 Use Linear Pair of angles:Two angles that are adjacent (share a leg) and supplementary (add up to 180°)

10:25 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

11:36 Proof

12:02 Use property of parallelogram:In a parallelogram, pair of opposite sides are equal.

13:34 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

11:46 (i) quadrilateral ABED is a parallelogram

12:06 Apply property of parallelogram:In a parallelogram, pair of opposite sides are equal.

13:17 (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.

19:34 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

20:13 Property of Trapezium states that it has only one pair of parallel sides.Non parallel sides are equal.

20:44 Construction to solve the problem

21:57 Isosceles Triangle Theorem. If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

22:27 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

CBSE class 9 maths chapter 8 Quadrilaterals

CBSE class 9 maths NCERT Solutions chapter 8 Quadrilaterals

Solutions for CBSE Class 9 Maths Chapter 8

NCERT solutions for class 9 maths Quadrilaterals

NCERT solutions for CBSE class 9 maths Quadrilaterals

CBSE Class 9 maths solutions Quadrilaterals

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properties of parallelograms

parallelogram properties geometry

Parallelogram Theorems Proof using Properties of Parallelogram

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