Quadrilaterals Application of Properties of Parallelogram to solve problems











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Quadrilaterals | Application of Properties of Parallelogram to solve problem • http://www.learncbse.in/ncert-solutio... • 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. • Follow us on Google Plus: • https://plus.google.com/+phanicbse • Like us on Facebook: •   / ncertsolutionsbooks   • Follow us on twitter •   / gyanpub   • • learncbse.in • CBSE solutions for class 9 maths Quadrilaterals • CBSE class 9 maths chapter 10 Quadrilaterals • CBSE class 9 maths NCERT Solutions chapter 10 Quadrilaterals

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