common core math 9-12.HSG-CO.C.11|Proofs involving Quadrilaterals|Prove theorems about parallelograms.

common core Quadrilaterals Properties of Parallelogram

00:02 common core math 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°.

03:11 common core math Quadrilaterals q2 If 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 Use property of Rectangle

07:58 common core math 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 common core math 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 common core math 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

33:22 common core math 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.

38:58 common core math 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.

45:15 common core math 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.

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.

52:31 common core math 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

01:02:55 common core math 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

01:06:03 common core math 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.

01:11:59 common core math 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

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