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- 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=50
^{o }then angle DPC is_________.

^{o }then angle DPC is_________.1)

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.

2)

Given, ∠A : ∠B : ∠C : ∠D = 3 : 7 : 6 : 4

Let ∠A = 3*x*, ∠B = 7*x*, ∠C = 6*x* and ∠D = 4*x*.

In quadrilateral ABCD,

∠A + ∠B + ∠C + ∠D = 360°

∴ 3*x* + 7*x* + 6*x* + 4*x* = 360°

⇒ 20*x* = 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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