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.
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.
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.
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).
(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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