- 1)THE FIGUREOBTAINED BY JOINING THE MID-POINTS OF THE SIDES OF A RHOMBUS ,TAKEN IN ORDER ,IS________.
- 2) IF ANGLES A,B,C AND D OF THE QUADRILATERAL ABCD ,TAKEN IN ORDER , ARE IN THE RATIO 3:7:6:4,THEN ABCD IS A __________.
- 3) THE DIAGONALS AC AND BD OF A RECTANGLE ABCD INTERSECT EACH OTHER AT P . IF angle ABD=50o then angle DPC is_________.
The figure obtained by joining the mid point of a rhombus is a rectangle.
Consider a rhombus PQRS, when its mid points are joined together, we get a rectangle ABCD.
Given, ∠A : ∠B : ∠C : ∠D = 3 : 7 : 6 : 4
Let ∠A = 3x, ∠B = 7x, ∠C = 6x and ∠D = 4x.
In quadrilateral ABCD,
∠A + ∠B + ∠C + ∠D = 360°
∴ 3x + 7x + 6x + 4x = 360°
⇒ 20x = 360°
⇒ x = 18°
∴ ∠A = 3 × 18° = 546
∠B = 7 × 18° = 126°
∠C = 6 × 18° = 108°
and ∠D = 4 × 18° = 72°
Now, ∠A + ∠B = 54° + 126° = 180°
and ∠C + ∠D = 108° + 72° = 180°
∴ AD || BC (If a transversal intersect two lines in such a way that a pair of consecutive interior angles are supplementary, then the two lines are parallel)
In the quadrilateral ABCD, the measure of all angles is different and AD || BC.
∴ Quadrilateral ABCD is a trapezium.
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